Independant domination number of a graph

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For notation and graph theory terminology in general we follow [6]. Goddard, Henning, Lyle and Southey [5] studied independent domination in regular graphs.

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Apr 6, - A dominating set of a graph G is a set S of vertices of G such that every vertex not in S is adjacent to a vertex in S. The domination number of G, denoted by γ (G), is the minimum size of a dominating set. A set is independent (or stable) if no two vertices in it are adjacent. domination numbers for several classes of graphs. Next we prove lower and upper bounds on the total outer-independent domination number of a graph, and.

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A dominating set of a graph G is a set S of vertices of G such that every vertex not in S is adjacent to a vertex in S. The domination number of G, denoted by γ(G), is the minimum size of a dominating set. A set is independent (or stable) if no two vertices in it are adjacent. A set S of vertices in a graph G is an independent dominating set of G if S is an independent set and every vertex not in S is adjacent to a vertex in S. In this.

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Dec 11, - Let G be a simple graph, and let p be a positive integer. A subset D⊆V(G) is a p-dominating set of the graph G, if every vertex v∈V(G)-D is. For a graph G, the definitions of domination number, denoted γ(G), and independent domination number, denoted i(G), are given, and the following results are.

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Vizing's conjecture is true for graphs G satisfying γi(G) = γ(G), where γ(G) is the domination number of a graph G and γi(G) is the independence-domination. Jump to Independent domination - Dominating sets are closely related to independent sets: an The independent domination number i(G) of a graph G is.

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Apr 10, - Sadly, this problem is NP-hard, hence there is no known polynomial time algorithm for this problem (and probably there is no way to find one. independent domination number in terms of maximal independent sets with minimum cardinality (i set). Further we consider vertex covering sets of graphs.

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Feb 4, - A set S of vertices in a graph G is an independent dominating set of G is adjacent to a vertex in S. The independent domination number of G. Abstract. Let G be a simple graph of order n, maximum degree ∆ and minimum degree δ ≥ 2. The independent domination number i(G) is defined to be.

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A set S of vertices in a graph G is called an independent dominating set if S is both independent and dominating. The independent domination number of G is. Allan and Laskar have shown that Kt.s-free graphs are graphs with equal domination and independent domination numbers. In this paper new classes of graphs.