Let γ(G), i(G), γS(G) and iS(G) denote the domination number, the independent domination number, the strong domination number and the independent strong domination number of a graph G, respectively. A graph G is called γi-perfect (domination perfect) if γ(H) = i(H), for every induced subgraph H of G. The classes of γγS-perfect, γSiS-perfect, iiS-perfect and γiS-perfect graphs are defined analog...

A vertex of a graph is said to dominate itself and all of its neighbors. A double dominating set of a graph G is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D. The double domination number of a graph G is the minimum cardinality of a double dominating set of G. For a graph G = (V,E), a subset D ⊆ V (G) is a 2dominating set if every vertex of V (...

4 In this paper, we study the domination number, the global dom5 ination number, the cographic domination number, the global co6 graphic domination number and the independent domination number 7 of all the graph products which are non-complete extended p-sums 8 (NEPS) of two graphs. 9

We initiate the study of total outer-independent domination in graphs. A total outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D, and the set V (G) \ D is independent. The total outer-independent domination number of a graph G is the minimum cardinality of a total outer-independent dominating set of G. First we discuss the ...

A dominating set in a graph G is a set S of vertices such that every vertex outside S has a neighbor in S; the domination number γ(G) is the minimum size of such a set. The independent domination number, written i(G), is the minimum size of a dominating set that also induces no edges. Henning and Southey conjectured that if G is a connected cubic graph with sufficiently many vertices, then i(G)...