Nordhaus-gaddum bounds for domination sums in graphs with specified minimum degree

Abstract

A set S ⊆ V is a dominating set in a graph G = (V, E) if each vertex in V-S is adjacent to at least one vertex in S. The domination number γ(G) is the minimum cardinality of a dominating set in G. We find improved bounds for γ(G) + γ(G) for graphs which have a given minimum degree.