THE INDEPENDENCE NUMBER OF CONNECTED (claw, $K_4$)-FREE 4-REGULAR GRAPHS

Abstract

An independent set of a graph $G$ is a subset of the vertices of $G$ such that no two vertices in the subset are joined by an edge in $G$. The independence number of $G$ is the cardinality of a maximum independent set of $G$. In this paper we give the exact value of the independence number for a (claw, $K_4$)-free 4-regular graph G without cut vertices.