Trees with Unique Minimum Semitotal Dominating Sets

Teresa W. Haynes; Michael A. Henning

doi:10.1007/s00373-020-02145-0

Trees with Unique Minimum Semitotal Dominating Sets

Teresa W. Haynes, Michael A. Henning

Mathematics and Applied Mathematics

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

7 Citations (Scopus)

Abstract

A set S of vertices in a graph G is a semitotal dominating set of G if it is a dominating set of G and every vertex in S is within distance 2 of another vertex of S. The semitotal domination number is the minimum cardinality of a semitotal dominating set of G. We observe that the semitotal domination number of a graph G falls between its domination number and its total domination number. We provide a characterization of trees that have a unique minimum semitotal dominating set.

Original language	English
Pages (from-to)	689-702
Number of pages	14
Journal	Graphs and Combinatorics
Volume	36
Issue number	3
DOIs	https://doi.org/10.1007/s00373-020-02145-0
Publication status	Published - 1 May 2020

Keywords

05C05
05C69
Semitotal domination
Trees

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1007/s00373-020-02145-0

Cite this

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AB - A set S of vertices in a graph G is a semitotal dominating set of G if it is a dominating set of G and every vertex in S is within distance 2 of another vertex of S. The semitotal domination number is the minimum cardinality of a semitotal dominating set of G. We observe that the semitotal domination number of a graph G falls between its domination number and its total domination number. We provide a characterization of trees that have a unique minimum semitotal dominating set.

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KW - Semitotal domination

KW - Trees

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IS - 3

ER -

Trees with Unique Minimum Semitotal Dominating Sets

Abstract

Keywords

ASJC Scopus subject areas

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