F.Y.B.Sc.

(Computer Science)
MTS-1152-P: Mathematics Practical-II
(NEP Based 2024 syllabus)
(Semester-II )
Practice slips

Slip No.:-1

Time: 3 hours Maximum Marks: 35

Q. 1 Attempt any TWO of the following using Python: [10M]

a) Draw a regular graph on 4 vertices with degree 2.

b) Draw symmetric directed graph on 6 vertices.

c) Let 𝐺1 and 𝐺2 be two graphs. Edge set of 𝐺1 = {(1,2), (2,3), (3,4), ((4,5)}and edge set of

𝐺2 = {(𝑎, 𝑏), (𝑏, 𝑐), (𝑐, 𝑑), (𝑏, 𝑑)} Draw union of Graph 𝐺1 and 𝐺2 .

Q. 2 Attempt any TWO of the following using Python: [10M]

a) Draw complete graph with 6 red colour vertices & node size 700.

b) Let 𝐺 be a graph with vertex set ={(1,2},(1,3),(4,3),(5,1),(4,5),(3,5)}. Determine whether

G is bipartite graph.

c) Dray any graph showing labelled vertices and edges with 6 vertices and 10 edges.

Q. 3 Attempt any TWO of the following using Python: [10M]

a) Verify Handshaking lemma for star graph on 7 vertices.

b) Draw the Petersen Graph. Determine whether it is 2-regular or 3-regular?

c) Draw balanced binary tree of height 4 with labelled vertices and edges.

Q. 4 Viva [5M]
 F.Y.B.Sc. (Computer Science)
MTS-1152-P: Mathematics Practical-II
(NEP Based 2024 syllabus)
(Semester-II )
Practice slips

Slip No.:-2

Time: 3 hours Maximum Marks: 35

Q. 1 Attempt any TWO of the following using Python: [10M]

a) Generate graph 𝐺 with vertex set {1,2,3,4,5} and edge set {(1,5), (1,3), (2,3),

(2,4), (3,4), (4,5)} Draw graph G.

b) Find degree of all vertices above graph G and determine whether it is connected graph?

c) Draw cycle graph 𝐶12 with blue color vertices and node size 800.

Q. 2 Attempt any TWO of the following using Python: [10M]

a) Let 𝐺1 and 𝐺2 be two graphs. Edge set of 𝐺1 = {(1,2), (2,3), (3,4), ((4,5), (1,4)}and edge set of

𝐺2 = {(𝑎, 𝑏), (𝑏, 𝑐), (𝑐, 𝑑), (𝑏, 𝑑), (𝑎, 𝑐} Draw intersection of Graph 𝐺1 and 𝐺2 .

b) Find eccentricity of every vertex in above graph 𝐺1 .

c) Find adjacency matrix and incidence matrix of above graph 𝐺2 .

Q. 3 Attempt any TWO of the following using Python: [10M]

a) Draw complete bipartite graphs 𝐾4,3 and 𝐾5,9 .

b) Draw any connected graph 𝐺. Determine whether 𝐺 is a tree.

c) Draw graph 𝐺 = {(𝑝, 𝑞), (𝑞, 𝑟), (𝑟, 𝑠), (𝑝, 𝑠)}. Determine whether 𝐺 is Eulerian graph.

Q. 4 Viva [5M]
 F.Y.B.Sc. (Computer Science)
MTS-1152-P: Mathematics Practical-II
(NEP Based 2024 syllabus)
(Semester-II )
Practice slips

Slip No.:-3

Time: 3 hours Maximum Marks: 35

Q. 1 Attempt any TWO of the following using Python: [10M]

a) Draw null graph on 12 vertices with vertex colour red and vertex size 600.

b) Draw any asymmetric directed graph on 10 vertices.

c) Draw ternary tree of heights 1 and 3.

Q. 2 Attempt any TWO of the following using Python: [10M]

a) Let 𝐺 be a graph with edge set {(1,3), (3,5), (5,6), (6,4), (4,2), (2,1)}. Find vertex

connectivity and edge connectivity of graph 𝐺.

b) Find center, radius and diameter of above graph 𝐺.

c) Draw complete bipartite graph 𝐾2,8.

Q. 3 Attempt any TWO of the following using Python: [10M]

a) Let 𝐺1 be a graph with edge set {(𝑎, 𝑏), (𝑐, 𝑑), (𝑎, 𝑒), (𝑏, 𝑓), (𝑎, 𝑓)}. Determine whether G is
connected graph?

b) Draw complement of above graph 𝐺1 . Determine whether the complement of 𝐺1 is

simple graph.

c) Find number of vertices, number of edges and degrees of all vertices in above graphs 𝐺1 .

Q. 4 Viva [5M]
 F.Y.B.Sc. (Computer Science)
MTS-1152-P: Mathematics Practical-II
(NEP Based 2024 syllabus)
(Semester-II )
Practice slips

Slip No.:-4

Time: 3 hours Maximum Marks: 35

Q. 1 Attempt any TWO of the following using Python: [10M]

a) Generate graph 𝐺 with vertex set {𝑣, 𝑤, 𝑥, 𝑦, 𝑧} and edge set {𝑒1 = (𝑣, 𝑤), 𝑒2 = (𝑥, 𝑦), 𝑒3 =
(𝑤, 𝑧), 𝑒4 = (𝑣, 𝑧), 𝑒5 = (𝑥, 𝑧)}. Draw graph 𝐺 showing labeled vertices and edges.

b) Find the number of components in above graph 𝐺.

c) From above graph 𝐺, delete edge 𝑒1 & 𝑒4 .

Q. 2 Attempt any TWO of the following using Python: [10M]

a) Draw any connected graph 𝐺. Determine whether it is Hamiltonian graph?

b) Draw 4 − 𝑎𝑟𝑦 tree of height 4.

c) Find all bridges and cut vertices in any graph 𝐺 with 6 vertices and 6 edges.

Q. 3 Attempt any TWO of the following using Python: [10M]

a) Draw wheel graphs 𝑊10 , 𝑊18 with blue colour of vertices.

b) Draw 𝐾5 , 𝐻 = 𝑐𝑜𝑚𝑝𝑙𝑒𝑚𝑒𝑛𝑡 𝑜𝑓 𝑁5 . Determine whether 𝐾5 is isomorphic to 𝐻?

c) Find the number of components in graph 𝑁5 .

Q. 4 Viva [5M]
 F.Y.B.Sc. (Computer Science)
MTS-1152-P: Mathematics Practical-II
(NEP Based 2024 syllabus)
(Semester-II )
Practice slips

Slip No.:-5

Time: 3 hours Maximum Marks: 35

Q. 1 Attempt any TWO of the following using Python: [10M]

a) Generate graph 𝐺 with vertex set {1,2,3,4,5} and edge set

{(4,5), (5,3), (2,2), (2,3), (2,4), (3,4), (1,5)}. Draw graph 𝐺 with vertices in red colour and

edges in green.

b) Verify Handshaking lemma for above graph 𝐺.

c) Draw regular graph on 5 vertices with degree 3.

Q. 2 Attempt any TWO of the following using Python: [10M]

a) Create any simple graph 𝐺1 . Find adjacency and incidence matrix of 𝐺1 .

b) Let 𝐺2 = 𝐾4 and 𝐺3 = 𝑁4 . Find intersection of 𝐺2 𝑎𝑛𝑑 𝐺3 .

c) Draw wheel graphs 𝑊21 𝑎𝑛𝑑 𝑊30.

Q. 3 Attempt any TWO of the following using Python: [10M]

a) Draw any graph 𝑇 containing 8 number of vertices and 7 edges.

b) Find center and radius of above tree 𝑇.

c) Find number of vertices and edges in above tree 𝑇.

Q. 4 Viva [5M]
 F.Y.B.Sc. (Computer Science)
MTS-1152-P: Mathematics Practical-II
(NEP Based 2024 syllabus)
(Semester-II )
Practice slips

Slip No.:-6

Time: 3 hours Maximum Marks: 35

Q. 1 Attempt any TWO of the following using Python: [10M]

a) Draw any graph 𝑇 with 8 vertices and 7 edges with labeled vertex and give colour of

your choice.

b) Determine whether 𝑇 is binary tree?

c) Find center, radius and diameter of above tree 𝑇.

Q. 2 Attempt any TWO of the following using Python: [10M]

a) Generate graph 𝐺 with vertex set {𝑎, 𝑏, 𝑐, 𝑑} and edge set {(𝑎, 𝑏), (𝑐, 𝑑), (𝑎, 𝑐)}. Draw
graph 𝐺 with vertices in red colour and edges in green.

b) Add vertex 𝑒 and edges {(𝑏, 𝑐), (𝑐, 𝑑)} in above graph. Determine whether the new

obtained graph 𝐺1 is connected?

c) Draw all paths from vertex 𝑎 to 𝑑 in above graph 𝐺1 .

Q. 3 Attempt any TWO of the following using Python: [10M]

a) Draw regular graph on 6 vertices with degree 3. Label all vertices and edges.

b) Draw Petersen graph. Determine whether it is 2-regular or 3-regular?

c) Verify Handshaking lemma for Petersen Graph.

Q. 4 Viva [5M]
 F.Y.B.Sc. (Computer Science)
MTS-1152-P: Mathematics Practical-II
(NEP Based 2024 syllabus)
(Semester-II )
Practice slips

Slip No.:-7

Time: 3 hours Maximum Marks: 35

Q. 1 Attempt any TWO of the following using Python: [10M]

a) Draw any symmetric directed graph on 7 vertices.

b) Draw complete bipartite graphs 𝐾4,2 , 𝐾5,6 , 𝐾2,6 .

c) Draw union of 𝐾2,2 and 𝐾3,3.

Q. 2 Attempt any TWO of the following using Python: [10M]

a) Create any simple graph 𝐺1 with nodes and edges in colours of your choice.

b) Determine whether 𝐺1 is bipartite?

c) Draw complement of above graph 𝐺1 and determine whether it is connected?

Q. 3 Attempt any TWO of the following using Python: [10M]

a) Generate graph 𝐺 with vertex set {1,2,3,4,5} and edge set

{(4,5), (5,3), (2,2), (2,3), (2,4), (3,4), (1,5)}. Draw graph 𝐺 with vertices in blue colour and

edges in red.

b) Find adjacency and incidence matrix for above graph 𝐺.

c) Find the number of vertices, number of edges and degree of all vertices in above graph 𝐺.

Q. 4 Viva [5M]
 F.Y.B.Sc. (Computer Science)
MTS-1152-P: Mathematics Practical-II
(NEP Based 2024 syllabus)
(Semester-II )
Practice slips

Slip No.:-8

Time: 3 hours Maximum Marks: 35

Q. 1 Attempt any TWO of the following using Python: [10M]

a) Draw star graph 𝐺 on 7 vertices with vertex size 600 and vertex colour orange.

b) Verify Handshaking lemma for above graph 𝐺.

c) Draw complement of above graph 𝐺. Determine whether the complement is simple graph?

Q. 2 Attempt any TWO of the following using Python: [10M]

a) Draw any complete asymmetric directed graph with 10 vertices and colours of your choice.

b) Draw union of graphs 𝑁7 and 𝑊12 .

c) Find the vertex connectivity and edge connectivity of the graph 𝐾5 and 𝐾4,5.

Q. 3 Attempt any TWO of the following using Python: [10M]

a) Draw a directed graph 𝐷1 with vertex set 𝑉 = {1,2,3,4,5} and directed edge set 𝐸 =
{(1,4), (2,3), (1,2), (5,3), (5,1), (4,1), (3,2), (5,2), (5,4)}. Draw underlying graph of
𝐷1 . Find in degree and out degree of all vertices in 𝐷1 .

b) Delete vertices {1,2} and edges {(5,3),(5,1)}from graph 𝐷1 .

c) Find adjacency and incidence matrix for Petersen graph.

Q. 4 Viva [5M]
 F.Y.B.Sc. (Computer Science)
MTS-1152-P: Mathematics Practical-II
(NEP Based 2024 syllabus)
(Semester-II )
Practice slips

Slip No.:-9

Time: 3 hours Maximum Marks: 35

Q. 1 Attempt any TWO of the following using Python: [10M]

a) Let graph 𝐺1 = 𝐶5 and 𝐺2 = 𝐾6 . Draw intersection of graph 𝐺1 𝑎𝑛𝑑 𝐺2 and name it as 𝐺3 .

b) Find all bridges, all cut vertices and cut sets in above graph 𝐺3 .

c) Find eccentricity of all vertices in graphs 𝐺1 and 𝐺2 .

Q. 2 Attempt any TWO of the following using Python: [10M]

a) Draw any connected graph 𝐺. Determine whether 𝐺 is a tree.

b) Draw spanning tree in above graph 𝐺.

c) Draw labelled regular graph on 4 vertices with degree two and give colours of your choice.

Q. 3 Attempt any TWO of the following using Python: [10M]

a) Generate graph 𝐺′ with vertex set {𝑎, 𝑏, 𝑐, 𝑑, 𝑒, 𝑓, 𝑔, ℎ} and edge set

{(𝑎, 𝑏), (𝑐, 𝑑), (𝑑, 𝑐), (𝑎, 𝑓), (𝑔, ℎ), (𝑒, 𝑒), (𝑎, ℎ), (𝑑, ℎ)}. Draw graph 𝐺′ with vertices in

red colour and edges in green.

b) Determine whether 𝐺′ is connected graph.

c) Draw the graph 𝐶5 , 𝑊6 , 𝐾4 , 𝐾4,3 , 𝑁6 .

Q. 4 Viva [5M]
 F.Y.B.Sc. (Computer Science)
MTS-1152-P: Mathematics Practical-II
(NEP Based 2024 syllabus)
(Semester-II )
Practice slips

Slip No.:-10

Time: 3 hours Maximum Marks: 35

Q. 1 Attempt any TWO of the following using Python: [10M]

a) Draw a directed graph 𝐷2 with vertex set 𝑉 = {1,2,3,4} and directed edge set 𝐸 =
{(1,4), (2,3), (1,2), (1,3), (4,1), (3,2)}. Draw underlying graph of 𝐷2 . Find in degree and

out degree of all vertices in 𝐷2 .

b) Determine whether 𝐷2 is connected. Find the number of components in above graph 𝐷2 .

c) Draw Petersen Graph and verify handshaking lemma for Petersen graph.

Q. 2 Attempt any TWO of the following using Python: [10M]

a) Draw a star graph on 5 vertices and regular graph on 7 vertices with degree 6.

b) Let graph 𝐺1 = 𝑁5 and 𝐺2 = 𝑊6 . Draw product of graph 𝐺1 𝑎𝑛𝑑 𝐺2 and name it as 𝐺3 .

c) Find adjacency and incidence matric for graph 𝐺3 .

Q. 3 Attempt any TWO of the following using Python: [10M]

a) Draw simple graph G with labelled vertices and edges and give colours of your choice

b) Find center, radius and diameter of above graph 𝐺.

c) Draw balanced binary trees of heights 2,4 𝑎𝑛𝑑 5.

Q. 4 Viva [5M]
 F.Y.B.Sc. (Computer Science)
MTS-1152-P: Mathematics Practical-II
(NEP Based 2024 syllabus)
(Semester-II )
Practice slips

Slip No.:-11

Time: 3 hours Maximum Marks: 35

Q. 1 Attempt any TWO of the following using Python: [10M]

a) Generate graph 𝐺 with vertex set {1,2,3,4,5} and edge set

{(4,5), (5,3), (2,2), (2,3), (2,4), (3,4), (1,5)}. Draw graph 𝐺 with vertices in yellow colour

and edges in blue.

b) Draw spanning tree 𝑇 of above graph 𝐺.

c) Determine whether spanning tree 𝑇 of 𝐺 is a binary tree.

Q. 2 Attempt any TWO of the following using Python: [10M]

a) Generate any two graphs with names 𝐺1 and 𝐺2 . Draw union of it and name it as 𝐺3 .

b) Draw complement of above graph 𝐺3 .

c) Draw the graph 𝐶7 , 𝑊8 , 𝐾6 , 𝐾4,3 , 𝑁4

Q. 3 Attempt any TWO of the following using Python: [10M]

a) Draw any symmetric graph directed graph on 7 vertices, vertex size=700, vertex colour=red.

b) Draw any graph simple 𝐺′ with 6 vertices and determine whether it is Eulerian graph.

c) Find adjacency and incidence matrix of above graph 𝐺′.

Q. 4 Viva [5M]
 F.Y.B.Sc. (Computer Science)
MTS-1152-P: Mathematics Practical-II
(NEP Based 2024 syllabus)
(Semester-II )
Practice slips

Slip No.:-12

Time: 3 hours Maximum Marks: 35

Q. 1 Attempt any TWO of the following using Python: [10M]

a) Generate graph 𝐺 with vertex set {𝑤, 𝑥, 𝑦, 𝑧} and edge set {𝑒1 = (𝑥, 𝑤), 𝑒2 = (𝑥, 𝑦), 𝑒3 =
(𝑤, 𝑧), 𝑒4 = (𝑦, 𝑧), 𝑒5 = (𝑥, 𝑧)}. Draw graph 𝐺 showing labeled vertices and edges.

b) Determine whether 𝐺 is Hamiltonian graph.

c) Draw ternary trees of heights 1 and 3.

Q. 2 Attempt any TWO of the following using Python: [10M]

a) Create a simple graph 𝐺′. Draw 𝐻 =complement of 𝐺′. Determine whether 𝐻 is simple graph.

b) Find any three paths in above graph 𝐺′.

c) Draw any complete symmetric directed graph with 10 vertices and colours of your choice.

Q. 3 Attempt any TWO of the following using Python: [10M]

a) Draw Petersen graph. Determine whether it is 2-regular or 3-regular?

b) Draw 𝐾5 , 𝐻 = 𝑐𝑜𝑚𝑝𝑙𝑒𝑚𝑒𝑛𝑡 𝑜𝑓 𝑁5 . Determine whether 𝐾5 is isomorphic to 𝐻?

c) Draw adjacency and incidence matrix of complement of Petersen graph.

Q. 4 Viva [5M]
 F.Y.B.Sc. (Computer Science)
MTS-1152-P: Mathematics Practical-II
(NEP Based 2024 syllabus)
(Semester-II )
Practice slips

Slip No.:-13

Time: 3 hours Maximum Marks: 35

Q. 1 Attempt any TWO of the following using Python: [10M]

a) Draw complete graph 𝐺 with 6 red colour vertices & node size 700.

b) Verify Handshaking lemma for above graph 𝐺..

c) Draw any connected graph 𝐺. Determine whether it is Hamiltonian graph?

Q. 2 Attempt any TWO of the following using Python: [10M]

a) Let 𝐺 be a graph with vertex set ={(1,2},(1,3),(4,3),(5,1),(4,5),(3,5)}. Determine whether

G is bipartite graph.

b) Draw the Petersen Graph. Determine whether it is 2-regular or 3-regular?

c) Draw 4 − 𝑎𝑟𝑦 tree of height 4.

Q. 3 Attempt any TWO of the following using Python: [10M]

a) Find all bridges and cut vertices in any graph 𝐺 with 6 vertices and 6 edges.

b) Dray any graph showing labelled vertices and edges with 6 vertices and 10 edges.

c) Draw balanced binary tree of height 4 with labelled vertices and edges.

Q. 4 Viva [5M]
 F.Y.B.Sc. (Computer Science)
MTS-1152-P: Mathematics Practical-II
(NEP Based 2024 syllabus)
(Semester-II )
Practice slips

Slip No.:-14

Time: 3 hours Maximum Marks: 35

Q. 1 Attempt any TWO of the following using Python: [10M]

a) Draw a regular graph on 4 vertices with degree 2.

b) Find all bridges, all cut vertices and cut sets in above graph.

c) Find adjacency and incidence matrix for Petersen graph.

Q. 2 Attempt any TWO of the following using Python: [10M]

a) Draw 𝐾5 , 𝐻 = 𝑐𝑜𝑚𝑝𝑙𝑒𝑚𝑒𝑛𝑡 𝑜𝑓 𝑁5 . Determine whether 𝐾5 is isomorphic to 𝐻?

b) Draw symmetric directed graph on 6 vertices.

c) Draw the graph 𝐶10 , 𝑊3 , 𝐾5 , 𝐾4,5 , 𝑁8 .

Q. 3 Attempt any TWO of the following using Python: [10M]

a) Let 𝐺1 and 𝐺2 be two graphs. Edge set of 𝐺1 = {(1,2), (2,3), (3,4), ((4,5)}and edge
set of 𝐺2 = {(𝑎, 𝑏), (𝑏, 𝑐), (𝑐, 𝑑), (𝑏, 𝑑)} Draw union of Graph 𝐺1 and 𝐺2 .

b) Draw any graph 𝑇 with 8 vertices and 7 edges with labeled vertex and give colour of

your choice.

c) Determine whether 𝑇 is binary tree?

Q. 4 Viva [5M]
 F.Y.B.Sc. (Computer Science)
MTS-1152-P: Mathematics Practical-II
(NEP Based 2024 syllabus)
(Semester-II )
Practice slips

Slip No.:-15

Time: 3 hours Maximum Marks: 35

Q. 1 Attempt any TWO of the following using Python: [10M]

a) Let 𝐺1 be a graph with edge set {(𝑎, 𝑏), (𝑐, 𝑑), (𝑎, 𝑒), (𝑏, 𝑓), (𝑎, 𝑓)}. Determine whether G is
connected graph?

b) Draw complement of above graph 𝐺1 . Determine whether the complement of 𝐺1 is

simple graph.

c) Find number of vertices, number of edges and degrees of all vertices in above graphs 𝐺1 .

Q. 2 Attempt any TWO of the following using Python: [10M]

a) Generate any two graphs 𝐺1 and 𝐺2 . Determine whether 𝐺1 is isomorphic to 𝐺2 .

b) Draw star graph 𝐺 on 7 vertices with vertex size 600 and vertex colour orange.

c) Verify Handshaking lemma for above graph 𝐺.

Q. 3 Attempt any TWO of the following using Python: [10M]

a) Let 𝐺1 be a graph with edge set {(𝑎, 𝑏), (𝑐, 𝑑), (𝑎, 𝑒), (𝑏, 𝑓), (𝑎, 𝑓)}. Determine whether G is
connected graph?

b) Draw complement of above graph 𝐺1 . Determine whether the complement of 𝐺1 is

simple graph.

c) Find number of vertices, number of edges and degrees of all vertices in above graphs 𝐺1 .

Q. 4 Viva [5M]
 F.Y.B.Sc. (Computer Science)
MTS-1152-P: Mathematics Practical-II
(NEP Based 2024 syllabus)
(Semester-II )
Practice slips

Slip No.:-16

Time: 3 hours Maximum Marks: 35

Q. 1 Attempt any TWO of the following using Python: [10M]

a) Draw any graph 𝑇 with 7 vertices and 10 edges with labeled vertex and give colour of

your choice.

b) Determine whether 𝑇 is binary tree?

c) Find center, radius and diameter of above tree 𝑇.

Q. 2 Attempt any TWO of the following using Python: [10M]

a) Generate graph 𝐺 with vertex set {𝑎, 𝑏, 𝑐, 𝑑, 𝑒} and edge set {(𝑎, 𝑏), (𝑐, 𝑑), (𝑎, 𝑐), (𝑐, 𝑒)}.

Draw graph 𝐺 with vertices in red colour and edges in green.

b) Add vertex 𝑓 and edges {(𝑏, 𝑓), (𝑐, 𝑓)} in above graph. Determine whether the new

obtained graph 𝐺1 is connected?

c) Draw all paths from vertex 𝑎 to 𝑑 in above graph 𝐺1 .

Q. 3 Attempt any TWO of the following using Python: [10M]

a) Draw regular graph on 5 vertices with degree 4. Label all vertices and edges.

b) Draw Petersen graph. Determine whether it is 2-regular or 3-regular?

c) Verify Handshaking lemma for Petersen Graph.

Q. 4 Viva [5M]
 F.Y.B.Sc. (Computer Science)
MTS-1152-P: Mathematics Practical-II
(NEP Based 2024 syllabus)
(Semester-II )
Practice slips

Slip No.:-17

Time: 3 hours Maximum Marks: 35

Q. 1 Attempt any TWO of the following using Python: [10M]

a) Create any simple graph 𝐺1 . Find adjacency and incidence matrix of 𝐺1 .

b) Let 𝐺2 = 𝐾5 and 𝐺3 = 𝑁7 . Find union of 𝐺2 𝑎𝑛𝑑 𝐺3 .

c) Draw wheel graphs 𝑊12 𝑎𝑛𝑑 𝑊20 .

Q. 2 Attempt any TWO of the following using Python: [10M]

a) Generate graph 𝐺 with vertex set {1,2,3,4,5} and edge set

{(4,5), (5,3), (2,1), (2,3), (2,4), (3,4), (1,5)}. Draw graph 𝐺 with vertices in red colour and

edges in green.

b) Verify Handshaking lemma for above graph 𝐺.

c) Draw balanced binary trees of heights 2,4 𝑎𝑛𝑑 5.

Q. 3 Attempt any TWO of the following using Python: [10M]

a) Generate graph 𝐺 with vertex set {𝑣, 𝑤, 𝑥, 𝑦, 𝑧} and edge set {𝑒1 = (𝑣, 𝑤), 𝑒2 = (𝑥, 𝑦), 𝑒3 =
(𝑤, 𝑧), 𝑒4 = (𝑣, 𝑧), 𝑒5 = (𝑥, 𝑧)}. Draw graph 𝐺 showing labeled vertices and edges.

b) Find adjacency and incidence matrix for above graph 𝐺.

c) Find the number of vertices, number of edges and degree of all vertices in above graph 𝐺.

Q. 4 Viva [5M]
 F.Y.B.Sc. (Computer Science)
MTS-1152-P: Mathematics Practical-II
(NEP Based 2024 syllabus)
(Semester-II )
Practice slips

Slip No.:-18

Time: 3 hours Maximum Marks: 35

Q. 1 Attempt any TWO of the following using Python: [10M]

a) Let graph 𝐺1 = 𝐶6 and 𝐺2 = 𝐾3 . Draw intersection of graph 𝐺1 𝑎𝑛𝑑 𝐺2 and name it as 𝐺3 .

b) Find all bridges, all cut vertices and cut sets in above graph 𝐺3 .

c) Find eccentricity of all vertices in graphs 𝐺1 and 𝐺2 .

Q. 2 Attempt any TWO of the following using Python: [10M]

a) Draw star graph 𝐺 on 7 vertices with vertex size 600 and vertex colour orange.

b) Verify Handshaking lemma for above graph 𝐺.

c) Draw complement of above graph 𝐺. Determine whether the complement is simple graph?

Q. 3 Attempt any TWO of the following using Python: [10M]

a) Generate graph 𝐺 with vertex set {1,2,3,4,5} and edge set

{(4,5), (5,3), (2,2), (2,3), (2,4), (3,4), (1,5)}. Draw graph 𝐺 with vertices in blue colour and

edges in red.

b) Find adjacency and incidence matrix for above graph 𝐺.

c) Find the number of vertices, number of edges and degree of all vertices in above graph 𝐺.

Q. 4 Viva [5M]
 F.Y.B.Sc. (Computer Science)
MTS-1152-P: Mathematics Practical-II
(NEP Based 2024 syllabus)
(Semester-II )
Practice slips

Slip No.:-19

Time: 3 hours Maximum Marks: 35

Q. 1 Attempt any TWO of the following using Python: [10M]

a) Generate graph 𝐺′ with vertex set {𝑎, 𝑏, 𝑐, 𝑑, 𝑒, 𝑓, 𝑔, ℎ} and edge set

{(𝑎, 𝑏), (𝑐, 𝑑), (𝑑, 𝑐), (𝑎, 𝑓), (𝑔, ℎ), (𝑒, 𝑒), (𝑎, ℎ), (𝑑, ℎ)}. Draw graph 𝐺′ with vertices in

red colour and edges in green.

b) Determine whether 𝐺′ is connected graph.

c) Draw the graph 𝐶5 , 𝑊6 , 𝐾4 , 𝐾4,3 , 𝑁6 .

Q. 2 Attempt any TWO of the following using Python: [10M]

a) Create any simple graph 𝐺1 . Find adjacency and incidence matrix of 𝐺1 .

b) Let 𝐺2 = 𝐾4 and 𝐺3 = 𝑁4 . Find intersection of 𝐺2 𝑎𝑛𝑑 𝐺3 .

c) Draw wheel graphs 𝑊21 𝑎𝑛𝑑 𝑊30.

Q. 3 Attempt any TWO of the following using Python: [10M]

a) Draw null graph on 12 vertices with vertex colour red and vertex size 600.

b) Draw any asymmetric directed graph on 10 vertices.

c) Draw ternary tree of heights 1 and 3.

Q. 4 Viva [5M]
 F.Y.B.Sc. (Computer Science)
MTS-1152-P: Mathematics Practical-II
(NEP Based 2024 syllabus)
(Semester-II )
Practice slips

Slip No.:-20

Time: 3 hours Maximum Marks: 35

Q. 1 Attempt any TWO of the following using Python: [10M]

a) Generate graph 𝐺 with vertex set {𝑎, 𝑏, 𝑐, 𝑑, 𝑒} and edge set {(𝑎, 𝑏), (𝑐, 𝑑), (𝑎, 𝑐), (𝑐, 𝑒)}.

Draw graph 𝐺 with vertices in red colour and edges in green.

b) Add vertex 𝑓 and edges {(𝑏, 𝑓), (𝑐, 𝑓)} in above graph. Determine whether the new

obtained graph 𝐺1 is connected?

c) Draw all paths from vertex 𝑎 to 𝑑 in above graph 𝐺1 .

Q. 2 Attempt any TWO of the following using Python: [10M]

a) Draw any connected graph 𝐺. Determine whether 𝐺 is a tree.

b) Draw spanning tree in above graph 𝐺.

c) Draw labelled regular graph on 4 vertices with degree two and give colours of your choice.

Q. 3 Attempt any TWO of the following using Python: [10M]

a) Draw regular graph on 6 vertices with degree 3. Label all vertices and edges.

b) Draw Petersen graph. Determine whether it is 2-regular or 3-regular?

c) Verify Handshaking lemma for Petersen Graph.

Q. 4 Viva [5M]
 F.Y.B.Sc. (Computer Science)
MTS-1152-P: Mathematics Practical-II
(NEP Based 2024 syllabus)
(Semester-II )
Practice slips

Slip No.:-21

Time: 3 hours Maximum Marks: 35

Q. 1 Attempt any TWO of the following using Python: [10M]

a) Draw any graph 𝑇 with 8 vertices and 7 edges with labeled vertex and give colour of

your choice.

b) Determine whether 𝑇 is binary tree?

c) Find center, radius and diameter of above tree 𝑇.

Q. 2 Attempt any TWO of the following using Python: [10M]

a) Create a simple graph 𝐺′. Draw 𝐻 =complement of 𝐺′. Determine whether 𝐻 is simple graph.

b) Find any three paths in above graph 𝐺′.

c) Draw any complete symmetric directed graph with 10 vertices and colours of your choice.

Q. 3 Attempt any TWO of the following using Python: [10M]

a) Generate any two graphs with names 𝐺1 and 𝐺2 . Draw union of it and name it as 𝐺3 .

b) Draw complement of above graph 𝐺3 .

c) Draw the graph 𝐶7 , 𝑊8 , 𝐾6 , 𝐾4,3 , 𝑁4

Q. 4 Viva [5M]
 F.Y.B.Sc. (Computer Science)
MTS-1152-P: Mathematics Practical-II
(NEP Based 2024 syllabus)
(Semester-II )
Practice slips

Slip No.:-22

Time: 3 hours Maximum Marks: 35

Q. 1 Attempt any TWO of the following using Python: [10M]

a) Draw complete bipartite graphs 𝐾4,3 and 𝐾5,9 .

b) Draw any connected graph 𝐺. Determine whether 𝐺 is a tree.

c) Draw graph 𝐺 = {(𝑝, 𝑞), (𝑞, 𝑟), (𝑟, 𝑠), (𝑝, 𝑠)}. Determine whether 𝐺 is Eulerian graph.

Q. 2 Attempt any TWO of the following using Python: [10M]

a) Generate graph 𝐺′ with vertex set {1,2,3,4,5} and edge set {(1,5), (1,3), (2,3),

(2,4), (3,4), (4,5)} Draw graph G’.

b) Find degree of all vertices above graph G’ and determine whether it is connected graph?

c) Draw cycle graph 𝐶12 with blue color vertices and node size 800.

Q. 3 Attempt any TWO of the following using Python: [10M]

a) Let 𝐺1 and 𝐺2 be two graphs. Edge set of 𝐺1 = {(1,2), (2,3), (3,4), ((4,5), (1,4)}and edge set of

𝐺2 = {(𝑎, 𝑏), (𝑏, 𝑐), (𝑐, 𝑑), (𝑏, 𝑑), (𝑎, 𝑐} Draw intersection of Graph 𝐺1 and 𝐺2 .

b) Find eccentricity of every vertex in above graph 𝐺1 .

c) Find adjacency matrix and incidence matrix of above graph 𝐺2 .

Q. 4 Viva [5M]

Slip No.:-23
 F.Y.B.Sc. (Computer Science)
MTS-1152-P: Mathematics Practical-II
(NEP Based 2024 syllabus)
(Semester-II )
Practice slips

Time: 3 hours Maximum Marks: 35

Q. 1 Attempt any TWO of the following using Python: [10M]

a) Generate graph 𝐺 with vertex set {1,2,3,4,5} and edge set {(1,5), (1,3), (2,3),

(2,4), (3,4), (4,5)} Draw graph G.

b) Find degree of all vertices above graph G and determine whether it is connected graph?

c) Draw cycle graph 𝐶31 with blue color vertices and node size 1000.

Q. 2 Attempt any TWO of the following using Python: [10M]

a) Let 𝐺1 and 𝐺2 be two graphs. Edge set of 𝐺1 = {(1,2), (2,3), (3,4), ((4,5), (1,4)}and edge set of

𝐺2 = {(𝑎, 𝑏), (𝑏, 𝑐), (𝑐, 𝑑), (𝑏, 𝑑), (𝑎, 𝑐} Draw union of Graph 𝐺1 and 𝐺2 .

b) Find eccentricity of every vertex in above graph 𝐺2 .

c) Find adjacency matrix and incidence matrix of above graph 𝐺1 .

Q. 3 Attempt any TWO of the following using Python: [10M]

a) Draw complete bipartite graphs 𝐾5,3 and 𝐾5,9 .

b) Draw any connected graph 𝐺. Determine whether 𝐺 is a tree.

c) Draw graph 𝐺 = {(𝑝, 𝑞), (𝑞, 𝑟), (𝑟, 𝑠), (𝑝, 𝑠)}. Determine whether 𝐺 is Hamiltonian graph.

Q. 4 Viva [5M]
 F.Y.B.Sc. (Computer Science)
MTS-1152-P: Mathematics Practical-II
(NEP Based 2024 syllabus)
(Semester-II )
Practice slips

Slip No.:-24

Time: 3 hours Maximum Marks: 35

Q. 1 Attempt any TWO of the following using Python: [10M]

a) Draw any asymmetric directed graph on 10 vertices.

b) Draw complete bipartite graphs 𝐾2,2 , 𝐾8,6 , 𝐾2,6 .

c) Draw intersection of 𝐾2,2 and 𝐾3,3.

Q. 2 Attempt any TWO of the following using Python: [10M]

a) Create any simple graph 𝐺1 with nodes and edges in colours of your choice.

b) Determine whether 𝐺1 is connected?

c) Draw complement of above graph 𝐺1 and determine whether it is simple?

Q. 3 Attempt any TWO of the following using Python: [10M]

a) Generate graph 𝐺 with vertex set {1,2,3,4,5,6,7} and edge set

{(4,7), (5,3), (2,2), (2,3), (2,4), (3,4), (1,5), (3,6), (6,7)}. Draw graph 𝐺 with vertices in blue
colour and edges in red.

b) Find adjacency and incidence matrix for above graph 𝐺.

c) Find the number of vertices, number of edges and degree of all vertices in above graph 𝐺.

Q. 4 Viva [5M]

Slip No.:-25
 F.Y.B.Sc. (Computer Science)
MTS-1152-P: Mathematics Practical-II
(NEP Based 2024 syllabus)
(Semester-II )
Practice slips

Time: 3 hours Maximum Marks: 35

Q. 1 Attempt any TWO of the following using Python: [10M]

a) Draw any graph 𝑇 with 8 vertices and 9 edges with labeled vertex and give colour of

your choice.

b) Determine whether 𝑇 is binary tree?

c) Find center, radius and diameter of above tree 𝑇.

Q. 2 Attempt any TWO of the following using Python: [10M]

a) Generate graph 𝐺 with vertex set {𝑎, 𝑏, 𝑐, 𝑑, 𝑒} and edge set {(𝑎, 𝑏), (𝑐, 𝑑), (𝑎, 𝑐), (𝑐, 𝑒)}.

Draw graph 𝐺 with vertices in red colour and edges in green.

b) Add vertex 𝑓 and edges {(𝑏, 𝑓), (𝑐, 𝑓)} in above graph. Determine whether the new

obtained graph 𝐺1 is connected?

c) Draw all paths from vertex 𝑏 to 𝑓 in above graph 𝐺1 .

Q. 3 Attempt any TWO of the following using Python: [10M]

a) Draw regular graph on 8 vertices with degree 2. Label all vertices and edges.

b) Draw Petersen graph. Determine whether it is 2-regular or 3-regular?

c) Verify Handshaking lemma for Petersen Graph.

Q. 4 Viva [5M]