Augmenting a graph of minimum degree 2 to have two disjoint total dominating sets

Michael Dorfling; Wayne Goddard; Johannes H. Hattingh; Michael A. Henning

doi:10.1016/j.disc.2005.06.020

Augmenting a graph of minimum degree 2 to have two disjoint total dominating sets

Michael Dorfling, Wayne Goddard, Johannes H. Hattingh, Michael A. Henning

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

15 Citations (Scopus)

Abstract

A total dominating set of a graph is a set of vertices such that every vertex is adjacent to a vertex in the set. We show that given a graph of order n with minimum degree at least 2, one can add at most (n-2n)/4+O(logn) edges such that the resulting graph has two disjoint total dominating sets, and this bound is best possible.

Original language	English
Pages (from-to)	82-90
Number of pages	9
Journal	Discrete Mathematics
Volume	300
Issue number	1-3
DOIs	https://doi.org/10.1016/j.disc.2005.06.020
Publication status	Published - 6 Sept 2005
Externally published	Yes

Keywords

Domatic number
Graph augmentation
Total domination

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2005.06.020

Cite this

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abstract = "A total dominating set of a graph is a set of vertices such that every vertex is adjacent to a vertex in the set. We show that given a graph of order n with minimum degree at least 2, one can add at most (n-2n)/4+O(logn) edges such that the resulting graph has two disjoint total dominating sets, and this bound is best possible.",

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AU - Hattingh, Johannes H.

AU - Henning, Michael A.

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AB - A total dominating set of a graph is a set of vertices such that every vertex is adjacent to a vertex in the set. We show that given a graph of order n with minimum degree at least 2, one can add at most (n-2n)/4+O(logn) edges such that the resulting graph has two disjoint total dominating sets, and this bound is best possible.

KW - Domatic number

KW - Graph augmentation

KW - Total domination

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DO - 10.1016/j.disc.2005.06.020

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Augmenting a graph of minimum degree 2 to have two disjoint total dominating sets

Abstract

Keywords

ASJC Scopus subject areas

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