RESILIENT DOMINATION IN GRAPHS

Abstract

A resilient dominating set in a graph is a dominating set in which each vertex has at least one neighbor within the set and at least one neighbor outside the set, and the weakly induced subgraph of the set is connected. The smallest cardinality of such a set is the resilient domination number. This paper establishes fundamental properties of this parameter and determines its exact values for several graph families. Furthermore, resilient dominating sets are characterized for graphs constructed via the join, vertex corona, and edge corona operations, and corresponding bounds and explicit formulas for the resilient domination number are obtained.