ir-Excellent Graphs

Abstract

Terasa W. Haynes et. al. [7], introduced the concept of irredun-
dance in graphs. A subset S of V (G) is called an irredundant set of G if for every vertex u 2 S, pn[u; S] ̸= ϕ. The minimum (maximum)cardinality of a maximal irredundant set of G is called the irredundance number of G (upper irredundance number of G) and is denoted by ir(G)(IR(G)). A subset V (G) is called an ir-set if it is an irredundant set of G of cardinality ir(G). A vertex u 2 V (G) is called ir-good if u belongs to an ir-set of G. G is said to be ir-
excellent if every vertex of G is ir-good. In this paper, a study of the excellent graphs with respect to irredundance is initiated.