Some results on the super domination number of a graph II

Let [Formula: see text] be a simple graph. A dominating set of [Formula: see text] is a subset [Formula: see text] such that every vertex not in [Formula: see text] is adjacent to at least one vertex in [Formula: see text]. The cardinality of a smallest dominating set of [Formula: see text], denoted by [Formula: see text], is the domination number of [Formula: see text]. A dominating set [Formula: see text] is called a super dominating set of [Formula: see text], if for every vertex [Formula: see text], there exists [Formula: see text] such that [Formula: see text]. The cardinality of a smallest super dominating set of [Formula: see text], denoted by [Formula: see text], is the super domination number of [Formula: see text]. In this paper, we obtain more results on the super domination number of graphs which is modified by an operation on vertices. Also, we present some sharp bounds for super domination number of chain and bouquet of pairwise disjoint connected graphs.

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Journal
Discrete Mathematics Algorithms and Applications
Published
2024-10-22
DOI
https://doi.org/10.1142/s1793830924501155
Primary Topic
Advanced Graph Theory Research
Type
article
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article

Some results on the super domination number of a graph II

Nima Ghanbari
Discrete Mathematics Algorithms and Applications
Advanced Graph Theory Research
article

Some results on the super domination number of a graph II

Nima Ghanbari
article en

Abstract

Let [Formula: see text] be a simple graph. A dominating set of [Formula: see text] is a subset [Formula: see text] such that every vertex not in [Formula: see text] is adjacent to at least one vertex in [Formula: see text]. The cardinality of a smallest dominating set of [Formula: see text], denoted by [Formula: see text], is the domination number of [Formula: see text]. A dominating set [Formula: see text] is called a super dominating set of [Formula: see text], if for every vertex [Formula: see text], there exists [Formula: see text] such that [Formula: see text]. The cardinality of a smallest super dominating set of [Formula: see text], denoted by [Formula: see text], is the super domination number of [Formula: see text]. In this paper, we obtain more results on the super domination number of graphs which is modified by an operation on vertices. Also, we present some sharp bounds for super domination number of chain and bouquet of pairwise disjoint connected graphs.

Discrete Mathematics Algorithms and ApplicationsVol. 17(07)
University of Bergen (NO)
Openalex Percentile: Top 78%
Advanced Graph Theory Research
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Some results on the super domination number of a graph II — Nima Ghanbari · Discrete Mathematics Algorithms and Applications (2024) | TGRS Research Map | TGRS