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

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

top

## Abstract

top
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

## How to cite

top

Changiz 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
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. [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. [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. [3] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998). Zbl0890.05002
4. [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. [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).

## NotesEmbed?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.