Characterization of Cubic Graphs G with irt(G) = Irt(G) = 2

摘要

A subset S of vertices in a graph G is called a total irredundant set if, for each vertex v in G, v or one of its neighbors has no neighbor in S ?{v}. The total irredundance number, ir(G), is the minimum cardinality of a maximal total irredundant set of G, while the upper total irredundance number, IR(G), is the maximum cardinality of a such set. In this paper we characterize all cubic graphs G with ir_(t)(G) = IR_(t)(G) = 2.