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 irt(G) = IRt(G) = 2
@article{bwmeta1.element.doi-10_7151_dmgt_1749, author = {Changiz Eslahchi and Shahab Haghi and Nader Jafari}, title = { Characterization of Cubic Graphs G with ir t (G) = Ir t (G) = 2 }, journal = {Discussiones Mathematicae Graph Theory}, volume = {34}, year = {2014}, pages = {559-565}, zbl = {1305.05173}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1749} }
Changiz Eslahchi; Shahab Haghi; Nader Jafari. Characterization of Cubic Graphs G with ir t (G) = Ir t (G) = 2 . Discussiones Mathematicae Graph Theory, Tome 34 (2014) pp. 559-565. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1749/
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