… exist graphs G with order n and δ ( G ) ≥ 1 for which γ [ 1 , 2 ] ( G ) = n . In this section, we will
find more graphs G of order n with γ [ 1 , 2 ] ( G … for [ 1 , 2 ] -domination number in Section 3. …

… Next we define the graph H f of order | V 1 f | , where V ( H f ) = V ( V 1 f ) and two vertices x
and y of V ( H f ) are adjacent in H f if there is a vertex v ∈ V 0 ″ f adjacent to both x and y in …

… graph definition of secondary domination by Hedetniemi et al., we extend the concept to
digraphs. Here, we define a (1, 2)domination graph … , X and y form a (1, 2)-dominating pair if and …

… In [5] Harary and Haynes defined a generalization of domination as follows: a subset S of V
… k −1 neighbors in S or v is in V − S and has at least k neighbors in S. The k-tuple domination …

… k = 1 we note simply that since G is connected S, must be independent and so by Lemma 3,
d, < 3. Now assume k > 2 and d, > 3k + 1. … for k = 1 as can be seen from the lirst graph in Fig. …

… However, we will see that there exist an infinite number of graphs with no total [1, 2… 1, 2]-set
in a graph G, we denote γt[1,2](G)=+∞. By this convention, it is trivial to see that for any graph …

… In the same way we can define an independent (1,2) -set to be a (1,2) -… graphs have
domination number at least 2, since this is an obvious necessary condition to have a γ -set that is a (1…

… ]-domination in interval graphs is still outstanding. In this paper… a minimum [1, 2] on non-proper
interval graphs by a dynamic … minimum [1, 2]-dominating set problem on circle graphs is …

… 1, we define a dumb-bell D n1Yn2Yk to be the graph of order nn1 n2 k À 1 and size qn 1
obtained from L n1Yk by attaching a cycle of length n2 to the end-vertex of L n1Yk ; that is, D …

… The p-domination number γ p ( G ) is the minimum … 1-domination number γ 1 ( G ) is the
usual domination number γ ( G ) . This definition immediately leads to the inequality γ ( G ) ⩽ γ 2 ( …