Invertibility in Well-Covered and Perfect Graphs

Abstract

Vertex cover is important to solve problems in developing and organizing intercommunication framework. A set of vertices of a graph is called a vertex cover, if this set covers all the edges in a graph. The minimum cardinality of such a set is called the covering number. In this paper, characterizations for a graph to possess inverse vertex covers are presented. Furthermore, the connection between well-covered graphs and different kinds of perfect graphs with invertibility is given.