# Characterization of Cubic Graphs G with ir t (G) = Ir t (G) = 2

Changiz Eslahchi; Shahab Haghi; Nader Jafari

Discussiones Mathematicae Graph Theory (2014)

- Volume: 34, Issue: 3, page 559-565
- ISSN: 2083-5892

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topChangiz Eslahchi, Shahab Haghi, and Nader Jafari. " Characterization of Cubic Graphs G with ir t (G) = Ir t (G) = 2 ." Discussiones Mathematicae Graph Theory 34.3 (2014): 559-565. <http://eudml.org/doc/268264>.

@article{ChangizEslahchi2014,

abstract = {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},

author = {Changiz Eslahchi, Shahab Haghi, Nader Jafari},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {total domination; total irredundance; cubic},

language = {eng},

number = {3},

pages = {559-565},

title = { Characterization of Cubic Graphs G with ir t (G) = Ir t (G) = 2 },

url = {http://eudml.org/doc/268264},

volume = {34},

year = {2014},

}

TY - JOUR

AU - Changiz Eslahchi

AU - Shahab Haghi

AU - Nader Jafari

TI - Characterization of Cubic Graphs G with ir t (G) = Ir t (G) = 2

JO - Discussiones Mathematicae Graph Theory

PY - 2014

VL - 34

IS - 3

SP - 559

EP - 565

AB - 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

LA - eng

KW - total domination; total irredundance; cubic

UR - http://eudml.org/doc/268264

ER -

## References

top- [1] O. Favaron, T.W. Haynes, S.T. Hedetniemi, M.A. Henning and D.J. Knisley, Total irredundance in graphs, Discrete Math. 256 (2002) 115-127. doi:10.1016/S0012-365X(00)00459-3[Crossref] Zbl1007.05074
- [2] T.W. Haynes, S.T. Hedetniemi, M.A. Henning and D.J. Knisley, Stable and unstable graphs with total irredundance number zero, Ars Combin. 61 (2001) 34-46. Zbl1072.05556
- [3] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998). Zbl0890.05002
- [4] S.M. Hedetniemi, S.T. Hedetniemi and D.P. Jacobs, Total irredundance in graphs: theory and algorithms, Ars Combin. 35 (1993) 271-284. Zbl0840.05040
- [5] Q.X. Tu and Z.Q. Hu, Structures of regular graphs with total irredundance number zero, Math. Appl. (Wuhan) 18 (2005) 41-44 (in Chinese).

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