Pa be ot least one edge, whese One ond Uguter is be & oth fn Vo - wo thie: 3 a pontitten exist theufore arid disconneted 4 Conuvsly’ det Youre Ain &: ju ve be the ger of aL vous that jane Ajotnedh athy co a Sine wat auconneked Vi dou not Y Gnade al Verte e| 4. the Femaiaing Nectcas uid! a Se Va: wl fem oN, ta foie do oh BY ah Bag uence the partion: Module 02 galadan .ond Hamiteons O” giobh: 0” opeusien onde graphs d unten ‘Consider two graphs Guz O€9 and. 69: (v8, then the graph whose VUE Sek Ls V\UVg- and the “a Get Js EVEg fs cole’ the unten ®} Gand hg and t% Ls denvted by Gao / 4 GVGa = (UVa > YER) 4 t1__b be v(6)=$a, bei dy , edu ols f > V(Gr)= S br dey a t be, pes) = {a,bcydie4 a b tc a4 (G,UGp) = Fe, @2123s eu es eg 4 Let we a 1062 ANE otic cs i a0 gropha ae (Yn, yard ae Ee) then the qvabh whose Uouer Get fs his a See iu £Neg 'Ps cowed o a bf Gland Gand 1 ds denoted by SiN a= (vs NVe Ey NE2) G be distonnertedl graph ,loystder a 5 ( =. TanahCTD fs rcs a a &6 & G2 Vlei) = fa, b, 65,43 V(G2)- Sp dyey ¥6G) Gr) HLbid% EUG) = $e,,er,e3 eu Y 4 ey ; ECG.) ~fLeurte ec3 Gey a E(G@iN&r) = feyy 3. Re IG Gx a acs ar. ahs nq yur ©| Duro qxaphy Gaz (nes) and y= (aiE2) % qvaph Const ng 4 woder rd (ViUUs) and at edgtr that areth G (014 hur not tn both. ‘ (4) = Ve) ¥VCa2) 4 Eo ECq) u ElG) -E(@\)Nb(2) J 'b Mob vi a i M V k } op cA Va eS Vud MS VCG1) EXVVa Vay VurYs 3 VV LG2) 22M 2a uve 4 VWaduvlad = {NinV2,VaiVurvs 4 EG) < 8 arb, tid, is) fa 8G): ig hokidyaby | f BlEr) UElem)=Saibievdiergs gshsKilh. o , Ela) nE(ar)= Lary vA Ne 4 { 1 W. i ) E(o)= E(G\) velO2) - E(&.) nelor)g | eA o BY eLby deh gihik LY Ny assition A Graph & = (416) vd Sasdhto bh, wuboytophy Hit ts then ' 4D 4wo 4 i pe Oe 4, ave § dy = anudh graph . a b: 4 b Xe ae aM el! 9 ee Vu, ; cas, ‘ Gekarbic di er$1 43 Hye Lar be. 43 Wel cid, hy Hutt, = Las bis As 1H 99. eee Nu grabh wempered qvabh: Ey o ee pes os Hy=2a,b,c,d& cathy, t+ a oF | Meef cd, ey - decampssed ual AW ={arb,c) die y bie Us eee Nuw Deeb : >- Dehetton Let G= Cv, E) beyarabh 4h aaiam ef graph G, ther Gv v graph gal & whtoined by daleteng Pela Vi ren Hh er B On edge o| qraph & Shen G~@i Vf oe ®| graph & obtained by duit lean boa #1. age id. Ci ” e G Ga GQ-ce: 6. Fuston- A podr of venttUs Vi 4a Sn a G a said to be plused Jb true two wut wu © meploced by stra aww verker VU gush Hat an eploc. thot txcunt do Atha Vor Vy 61 ene a aauine Ft ; thay Vy or oO ko V ae es & 2 . = ‘ Gq (vive) We F ' | wy 4 1 14s 2.0 2 oe @ (142 6)¥, ah a | + Complemank =|_gnaph (e'enG) a cempiemank (4! 97 &) t hae du @(vie) be qroph 7 43 dehgned coo be a graph whiun hos Vas chs Se e\ Vota and tuo ENte4 ane adjacent In G af and enty 3} thay ax not aajanated fo Gon £9 jee b Sd (polaron x fea, Hei AV "Ne a : ») , x ee ein bce 6) —aS ae amar g.Sey Complemutt 24 groph G= (Ve) dh ~ on ih, at i somo why ¢ do Js complemen - eg Alani go d. Nefayb dy \6) =3 “4 e cen <6 (Eas Ysemowphr cg Self Compt VeSaib,c dy BDO Bal, acrshe cre cdsba , Beh empleo, mar Osa. bob, asc, 7 A 2] Seqy=Q 2 2Y deet.Sey~€1.2;2 03 dsq. a a a! iC 1G Vefarbicrdye,4) NVeQa thier dies J y 18) yn |) =9 Thus FORK Fs not § somprphi < A not Self Complementary . a(ereushondant at! edgy AbS or, adisbd , chit b ey Hk da Fsemstpryc ¢ cell @mplemuy , « A Unsed walk surnne Hip e) G exartly ONLe Buch 4 aot Ba aly Line. if eds existed Ahen Ge 5 Obed Eula graph. ; vA Note Edgus Wit exarely onu, vod may be Supented 5 Start Same ul P ae ES OG Re ! in a4 § éndiny) Liner should be PeysesiRegTesPe snes qe,p 1b. Cosed walk and ities euler line Sle i ale gyabh.Cc ») 7 s q Ee becdesc egb ce aeyal 5 eX) ae, mee tena , As thi, graph bY not closed wad 4 a ate eated . / Hb not Euler qsoph. bukit Ae, Bec € ey Des Cea Bey Degh C1oE eg F eqgh* ; lene LE dy closed walk and Hos exten Ue Ww ahr groph ay | “ an|| SEGANe Pe AeggezBeyRes APEPo “6 d 1 Pea , SE ds — wW ak & % ieee Terie 7, te oe elo graph iV, vrgB : 1G uh. Be ‘) QRACBAR PQ, oe i TR A c he 3 AM the edgis au sepeated sl % mot elun aoph A ce) one, Berreycegdes herd “ Be, DES Ay alk edges ane not in watk $ ai ; AdQu as sebeated a Ue, Wot ene q7aPh. a 4 \ Pogwe AgLB *) us t {LPs closed wotlk 4 wy Line: ‘ (yr lt wv ewe ! prabh An open men walk ou.ning Hhtouah asouy G Clankty ence , Suth a WOIK ds called “Untonual ( en etisied cated untwsyal graph et ar 7 Se oi cadeethed 3aup cg mugs, "lt wo open wask , , UNfusol lense SE DB Uniounsal cycaph shettin A Given Gmnected graph Sy: is on eal graph ca yy all votes oe G axe Bf even 3 ees Q 4% an exile graph Cendains eather Une. In 8 Oe a “1 w through too new e using one edge with we ( entgned another eye wilt, owes Reus leave. From iy vudexr We + CL ond (ye Cam enrer rte, that bourse Sr Yoxt. , _ voter an oth a ae a as etn dag a Vo 1) Ny 2-1 ted el Ks LoaNsaes Me ye, Ponsa suppose, a Ei enn “eh. eo use dear a, a mas a BUvery/ & o unt Lae Stank AMO ventory, ’ Sirce auiny veder wo of even degete WUUT enitey . into WU Vinfet 4 Uh prom Rams venkey, j Mrautng tenths unde wiearhing voter v. = & Contarns eit graph Theovem ‘ { In a Connuted guaph » with exatHy ak od Douto thou etd K edge-aisjotnt subgraphs él Thad they doquthvn Contain Olt edges 6} Gy and hg Sach st a uniweisal gpaph ae a re det wy denote the Ak odd’ wurdiers 163 6 by Ui Mo its Ue And Vv) Ve. 7 ae Conarden she edges “ee €ty,V,), eas (YoyVa) ef .OP8 Construct the Graph G' obtained HY Oding Freee eCdgu to Gi then’ exes VOL Of Gly of a © Wy Aeqre and ts thyuferts nn Cul ine and ALO Exile graph -. — Mek g Yo denoted os El ne fn. GF w eremep Sas = ek deus aiizhen™ul be 8 pitt trip X-oPen walks eaih ©) wohich ik @ Untdolnsal Une. These k-wobs are edge dis oint subg eiaph & aG Gnd thy togsthan tenatina ‘all oe i Anbitiantly THostobls 9Xobb rrnayensable) if | In Eulut’ graph’, avveiter V have a porobersty ui (AN ely line's alibdip ' ebtal madiushin, ons pele any walk vurter V Suh a qvoph i call “Astbrbrarutly: ‘ausasal AO KE sete N 4 eae é b, die is vik a GHbItavy Sse abide is VOU ah bl x Cdecobe C - £ ee chacdee) Hen Pha Arbitently boy abledec iS ¥w (f) as avthidanily Houable gap) Dy a, _ tt mot owotanily phoctabls KS quaiph Dfgnaph (Dineckeat groph] A Diseecked graph (or) Daqroph G tomas of as oh vertces Ve WiV2icdim and) edges = &@2.---- Huu as dination rom pass ef, sustices (vinv5) a i . In a digraph, vedtcer ae sepsusented by poirds é edqu by Une Seqrnurt bho WGN With’ an /asuieuy dinetted hom vi and Vy y ps Thou wu atyps of cen z xInde x OUEdignes, \. Dutdegtue’” the Numbess ef edges Pictduind ‘oud of a verter Vy Js cabled outdledeise tt ig denoted by do? (vi). 9% 2 Indegua's The numbex 4 tnetdsnt Pro a Veiey vy Js called Indegsee Bh wi att bs i 4 > iM) =1 Ouidegrer dtluiy= 3 avs) .a eats) = | ade HAV 2 ee) oa, = q i eee. By i] gt (vy)= 1 . corp AW) 23 owbios t ; arts): is s “qvs).0Note © In nany digraph Gy shy dum @] au radeon Fs equal to dum 6] di out arly - Ed (vi) ; ISolated Bouter! TE is a Veter Pr which ray and Oudegrot MU eQUdl do ZUL0. Rindund putter © ea potter Of, dears Value a(t, | [ndegues Ov Oukdegres) athuuuise FasaUt Sgn IF kwvo echaes ave mabppeol ento San, eat als of vot CL In aboue graph, Cs 05 (600 pomaite edgu Typeral dtgnaph Surtgone mol yonalisl ‘edgy ‘Simple dequoph A digraph Hot has nb bell, loobe. Poxaity Seal eh *s cabled Simple dtguabh a diqr aKe2 a. Agaeranstfie. an which "awn edqus Qo) tho ds ae 10) et & 3 3. Axuuramuth'c di © A digsaph thos hos adm! baie bch o pow eh BOLLS, hus ae atkowed +o have ell, Loch are volledt dtgrsabh. both eegnetass nite Clemente sone sree esieitie Sate Syst | Aloe liad Ble syrmenshteasek! te e a (@ 5. Stmple Arsumdtic dfgraph LA di h dhat is bot Stmphe 4 Amsumatrtc Ds Lotled &P @§ Auymtfe a: ae ey a c