The Slater and Sub-k-Domination Number of a Graph with Applications to Domination and k-Domination

Abstract

In this paper we introduce and study a new graph invariant derived from the degree sequence of a graph G, called the sub-k-domination number and denoted subk(G). This invariant serves as a generalization of the Slater number; in particular, we show that subk(G) is a computationally efficient sharp lower bound on the k-domination number of G, and improves on several known lower bounds. We also characterize the sub-k-domination numbers of several families of graphs, provide structural results on sub-k-domination, and explore properties of graphs which are subk(G)-critical with respect to addition and deletion of vertices and edges.

Keywords

• slater number
• domination number
• sub-k-domination number
• k-domination number
• degree sequence index strategy
• 05c69