Let G be a graph and (G) denote the domination number of G. A dominating set D of a graph G with |D|= (G) is called a -set of G. A vertex x of a graph G is called: (i) -fixed if x belongs to everyâ€¦ (More)

The domination number Î³(G) of a graph G is the minimum number of vertices in a set D such that every vertex of the graph is either in D or is adjacent to a member of D. Any dominating set D of aâ€¦ (More)

For a graphical property P and a graph G, a subset S of vertices of G is a P-set if the subgraph induced by S has the property P . The domination number with respect to the property P , denoted byâ€¦ (More)

The bondage number b(G) of a graph G is the smallest number of edges whose removal from G results in a graph with larger domination number. In this paper, we present new upper bounds for b(G) inâ€¦ (More)

Let Î³(G) and #Î³(G) denote the domination number and the number of all distinct minimum dominating sets of a graph G, respectively. We show that #Î³(G + e) â‰¥ #Î³(G) for every edge e âˆˆ E(G) with Î³(G+e) =â€¦ (More)

A subset D of vertices in a graph G is k-dependent if the maximum degree of a vertex in the subgraph ã€ˆDã€‰ induced by D is at most k. The kdependent domination number Î³(G) of a graph G is the minimumâ€¦ (More)