Vertices contained in all or in no minimum total dominating set of a tree

Ernest J. Cockayne; Michael A. Henning; Christina M. Mynhardt

doi:10.1016/s0012-365x(02)00447-8

Vertices contained in all or in no minimum total dominating set of a tree

Ernest J. Cockayne, Michael A. Henning, Christina M. Mynhardt

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

22 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. We characterize the set of vertices of a tree that are contained in all, or in no, minimum total dominating sets of the tree.

Original language	English
Pages (from-to)	37-44
Number of pages	8
Journal	Discrete Mathematics
Volume	260
Issue number	1-3
DOIs	https://doi.org/10.1016/s0012-365x(02)00447-8
Publication status	Published - 6 Jan 2003
Externally published	Yes

Keywords

Total domination
Total domination number
Tree

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/s0012-365x(02)00447-8

Cite this

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title = "Vertices contained in all or in no minimum total dominating set of a tree",

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. We characterize the set of vertices of a tree that are contained in all, or in no, minimum total dominating sets of the tree.",

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AU - Cockayne, Ernest J.

AU - Henning, Michael A.

AU - Mynhardt, Christina M.

PY - 2003/1/6

Y1 - 2003/1/6

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. We characterize the set of vertices of a tree that are contained in all, or in no, minimum total dominating sets of the tree.

AB - 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. We characterize the set of vertices of a tree that are contained in all, or in no, minimum total dominating sets of the tree.

KW - Total domination

KW - Total domination number

KW - Tree

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U2 - 10.1016/s0012-365x(02)00447-8

DO - 10.1016/s0012-365x(02)00447-8

M3 - Article

AN - SCOPUS:0037421163

SN - 0012-365X

VL - 260

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EP - 44

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 1-3

ER -

Vertices contained in all or in no minimum total dominating set of a tree

Abstract

Keywords

ASJC Scopus subject areas

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