On Double Domination Numbers of Generalized Petersen Graphs

Abstract

A ( total ) double dominating set in a graph G is a subset S ⊆ V ( G ) such that each vertex in V ( G ) is (total) dominated by at least 2 vertices in S. The ( total ) double domination number of G is the minimum size of a (total) double dominating set of G. We determine the total double domination numbers and give upper bounds for double domination numbers of generalized Petersen graphs. By applying an integer programming model for double domination numbers of a graph, we have determined some exact values of double domination numbers of these generalized Petersen graphs with small parameters. The result shows that the given upper bounds match these exact values.