Geodesic
Characterization of cubic graphs $G$ with $ir_t(G)=IR_t(G)=2$
Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 3, pp. 559-565

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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.
Keywords: total domination, total irredundance, cubic 
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Eslahchi, Changiz; Haghi, Shahab; Jafari Rad, Nader. Characterization of cubic graphs $G$ with $ir_t(G)=IR_t(G)=2$. Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 3, pp. 559-565. http://geodesic.mathdoc.fr/item/DMGT_2014_34_3_a7/