Total domination critical and stable graphs upon edge removal

Wyatt J. Desormeaux; Teresa W. Haynes; Michael A. Henning

doi:10.1016/j.dam.2010.06.003

Total domination critical and stable graphs upon edge removal

Wyatt J. Desormeaux, Teresa W. Haynes, Michael A. Henning

Mathematics and Applied Mathematics

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

A set S of vertices in a graph G is a total dominating set of G if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set of G is the total domination number of G. A graph is total domination edge critical if the removal of any arbitrary edge increases the total domination number. On the other hand, a graph is total domination edge stable if the removal of any arbitrary edge has no effect on the total domination number. In this paper, we characterize total domination edge critical graphs. We also investigate various properties of total domination edge stable graphs.

Original language	English
Pages (from-to)	1587-1592
Number of pages	6
Journal	Discrete Applied Mathematics
Volume	158
Issue number	15
DOIs	https://doi.org/10.1016/j.dam.2010.06.003
Publication status	Published - 6 Aug 2010

Keywords

Total domination edge critical
Total domination edge stable

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/j.dam.2010.06.003

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AU - Desormeaux, Wyatt J.

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AU - Henning, Michael A.

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N2 - A set S of vertices in a graph G is a total dominating set of G if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set of G is the total domination number of G. A graph is total domination edge critical if the removal of any arbitrary edge increases the total domination number. On the other hand, a graph is total domination edge stable if the removal of any arbitrary edge has no effect on the total domination number. In this paper, we characterize total domination edge critical graphs. We also investigate various properties of total domination edge stable graphs.

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KW - Total domination edge stable

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Total domination critical and stable graphs upon edge removal

Abstract

Keywords

ASJC Scopus subject areas

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