Domination and 2-degree-packing numbers in graphs
Abstract
A dominating set of a graph G is a set D⊂eq V(G) such that \-every vertex of G is either in D or is adjacent to a vertex in D. The domination number of G, γ(G), is the minimum order of a dominating set. A subset R of edges of a graph G is a 2-degree-packing, if any three edges from R do not have the same incident vertex. The 2-degree-packing number of G, 2(G), is the maximum order of a 2-degree-packing of G. In this paper, we prove that any simple graph G satisfies γ(G)≤2(G)-1. Furthermore, we give a characterization of simple connected graphs G satisfying γ(G)=2(G)-1.
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