Characterization of cubic graphs G with ir_{t}(G)=IR_{t}(G)=2
Changiz Eslahchi, Shahab Haghi, Nader Jafari Rad · Discussiones Mathematicae Graph Theory · 2014
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.