Inequalities between strong, weak domination numbers and chromatic number of a graph

Abstract

In this paper, upper bounds for the sums γα (G) + χ(G), and products γα(G)χ(G) are obtained, where γα(G) is the strong or the weak domination number and χ(G) is the chromatic number of a graph G. The extremal graphs are characterised. © 2018 Utilitas Mathematica Publishing Inc. All rights reserved.