On accurate domination in graphs

Joanna Cyman; Michael A. Henning; Jerzy Topp

doi:10.7151/dmgt.2182

On accurate domination in graphs

Joanna Cyman, Michael A. Henning, Jerzy Topp

Mathematics and Applied Mathematics

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

Abstract

A dominating set of a graph G is a subset D ⊆ V_G such that every vertex not in D is adjacent to at least one vertex in D. The cardinality of a smallest dominating set of G, denoted by γ(G), is the domination number of G. The accurate domination number of G, denoted by γ_a(G), is the cardinality of a smallest set D that is a dominating set of G and no |D|-element subset of V_G \ D is a dominating set of G. We study graphs for which the accurate domination number is equal to the domination number. In particular, all trees G for which γ_a(G) = γ(G) are characterized. Furthermore, we compare the accurate domination number with the domination number of different coronas of a graph.

Original language	English
Pages (from-to)	605-608
Number of pages	4
Journal	Discussiones Mathematicae - Graph Theory
Volume	39
Issue number	2
DOIs	https://doi.org/10.7151/dmgt.2182
Publication status	Published - 2019

Keywords

Accurate domination number
Corona
Domination number
Tree

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.7151/dmgt.2182

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AB - A dominating set of a graph G is a subset D ⊆ VG such that every vertex not in D is adjacent to at least one vertex in D. The cardinality of a smallest dominating set of G, denoted by γ(G), is the domination number of G. The accurate domination number of G, denoted by γa(G), is the cardinality of a smallest set D that is a dominating set of G and no |D|-element subset of VG \ D is a dominating set of G. We study graphs for which the accurate domination number is equal to the domination number. In particular, all trees G for which γa(G) = γ(G) are characterized. Furthermore, we compare the accurate domination number with the domination number of different coronas of a graph.

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On accurate domination in graphs

Abstract

Keywords

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