On the domination number of graphs with minimum degree six

Csilla Bujtás; Michael A. Henning

doi:10.1016/j.disc.2021.112449

On the domination number of graphs with minimum degree six

Csilla Bujtás
, Michael A. Henning

Mathematics and Applied Mathematics

University of Ljubljana

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

6 Citations (Scopus)

Abstract

A dominating set in a graph G is a set S of vertices such that every vertex that does not belong to S is adjacent to a vertex from it. The domination number γ(G) is the minimum cardinality of a dominating set in G. In this paper we prove that if G is a graph of order n with minimum degree at least 6, then [Formula presented]. This improves the best known bounds to date.

Original language	English
Article number	112449
Journal	Discrete Mathematics
Volume	344
Issue number	8
DOIs	https://doi.org/10.1016/j.disc.2021.112449
Publication status	Published - Aug 2021

Keywords

Domination in graphs
Minimum degree six
Upper bounds

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2021.112449

Cite this

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AB - A dominating set in a graph G is a set S of vertices such that every vertex that does not belong to S is adjacent to a vertex from it. The domination number γ(G) is the minimum cardinality of a dominating set in G. In this paper we prove that if G is a graph of order n with minimum degree at least 6, then [Formula presented]. This improves the best known bounds to date.

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KW - Upper bounds

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On the domination number of graphs with minimum degree six

Abstract

Keywords

ASJC Scopus subject areas

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