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

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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Bibliographic Details
Published in:Discrete mathematics 2003-01, Vol.260 (1), p.37-44
Main Authors: Cockayne, Ernest J., Henning, Michael A., Mynhardt, Christina M.
Format: Article
Language:English
Subjects:
Applied sciences
Combinatorics
Combinatorics. Ordered structures
Computer science
control theory
systems
Exact sciences and technology
Graph theory
Information retrieval. Graph
Mathematics
Sciences and techniques of general use
Theoretical computing
Total domination
Total domination number
Tree
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Description
Summary: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.
ISSN:0012-365X
1872-681X
DOI:10.1016/S0012-365X(02)00447-8