Characterization of Cubic Graphs G with ir_t(G) = Ir_t(G) = 2

• Autorzy: Changiz Eslahchi , Shahab Haghi , Nader Jafari
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

total domination; total irredundance; cubic

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2014
• Tom: 34
• Numer: 3
• Strony: 559-565

Daty

wydano

2014-08-01

otrzymano

2013-01-08

poprawiono

2013-06-03

zaakceptowano

2013-06-27

online

2014-07-16

Twórcy

autor

Changiz Eslahchi

• Department of Mathematics Shahid Beheshti University, G. C. Evin, Tehran, Iran

autor

Shahab Haghi

• Department of Mathematics Shahid Beheshti University, G. C. Evin, Tehran, Iran

autor

Nader Jafari

• Rad Department of Mathematics Shahrood University of Technology Shahrood, Iran

Bibliografia

• [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]
• [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.
• [3] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998).
• [4] S.M. Hedetniemi, S.T. Hedetniemi and D.P. Jacobs, Total irredundance in graphs: theory and algorithms, Ars Combin. 35 (1993) 271-284.
• [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).

Identyfikatory

DOI

10.7151/dmgt.1749