Properties of total domination edge-critical graphs

Michael A. Henning; Lucas C. van der Merwe

doi:10.1016/j.dam.2009.09.004

Properties of total domination edge-critical graphs

Michael A. Henning, Lucas C. van der Merwe

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

7 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 γ_t (G) of G. The graph G is total domination edge critical if for every edge e in the complement of G, γ_t (G + e) < γ_t (G). We call such graphs γ_t E C. Properties of γ_t E C graphs are established.

Original language	English
Pages (from-to)	147-153
Number of pages	7
Journal	Discrete Applied Mathematics
Volume	158
Issue number	2
DOIs	https://doi.org/10.1016/j.dam.2009.09.004
Publication status	Published - 28 Jan 2010
Externally published	Yes

Keywords

Bounds
Diameter
Edge critical
Total domination

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/j.dam.2009.09.004

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KW - Edge critical

KW - Total domination

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Properties of total domination edge-critical graphs

Abstract

Keywords

ASJC Scopus subject areas

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