<p>This paper explores the newly introduced concept of paired disjunctive domination, initially proposed by Henning et al. A subset <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$ D \subseteq V $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>D</mi> <mo>⊆</mo> <mi>V</mi> </mrow> </math></EquationSource> </InlineEquation> is called a disjunctive dominating set of a graph <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$ G $</EquationSource> <EquationSource Format="MATHML"><math> <mi>G</mi> </math></EquationSource> </InlineEquation> for each vertex <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$ v \in V $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>v</mi> <mo>∈</mo> <mi>V</mi> </mrow> </math></EquationSource> </InlineEquation>, if there exists either a vertex in <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$ D $</EquationSource> <EquationSource Format="MATHML"><math> <mi>D</mi> </math></EquationSource> </InlineEquation> adjacent to <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$ v $</EquationSource> <EquationSource Format="MATHML"><math> <mi>v</mi> </math></EquationSource> </InlineEquation>, or at least two vertices in <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$ D $</EquationSource> <EquationSource Format="MATHML"><math> <mi>D</mi> </math></EquationSource> </InlineEquation> whose distance from <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$ v $</EquationSource> <EquationSource Format="MATHML"><math> <mi>v</mi> </math></EquationSource> </InlineEquation> is exactly two in <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$ G $</EquationSource> <EquationSource Format="MATHML"><math> <mi>G</mi> </math></EquationSource> </InlineEquation>. Additionally, a disjunctive dominating set <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$ D \subseteq V $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>D</mi> <mo>⊆</mo> <mi>V</mi> </mrow> </math></EquationSource> </InlineEquation> is defined as a paired disjunctive dominating set if the induced subgraph by <InlineEquation ID="IEq10"> <EquationSource Format="TEX">$ D $</EquationSource> <EquationSource Format="MATHML"><math> <mi>D</mi> </math></EquationSource> </InlineEquation> in <InlineEquation ID="IEq11"> <EquationSource Format="TEX">$ G $</EquationSource> <EquationSource Format="MATHML"><math> <mi>G</mi> </math></EquationSource> </InlineEquation> contains a perfect matching. In this work, we present new results concerning the R-vertex, R-edge, R-vertex neighborhood, and R-edge neighborhood corona structures based on this parameter.</p>

Paired Disjunctive Domination on R-Corona Operations

期刊论文
发表日期：

2026年1月21日

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Hande Tuncel Golpek,
Aysun Aytac

摘要

This paper explores the newly introduced concept of paired disjunctive domination, initially proposed by Henning et al. A subset $ D \subseteq V $ $D \subseteq V$ is called a disjunctive dominating set of a graph $ G $ $G$ for each vertex $ v \in V $ $v \in V$ , if there exists either a vertex in $ D $ $D$ adjacent to $ v $ $v$ , or at least two vertices in $ D $ $D$ whose distance from $ v $ $v$ is exactly two in $ G $ $G$ . Additionally, a disjunctive dominating set $ D \subseteq V $ $D \subseteq V$ is defined as a paired disjunctive dominating set if the induced subgraph by $ D $ $D$ in $ G $ $G$ contains a perfect matching. In this work, we present new results concerning the R-vertex, R-edge, R-vertex neighborhood, and R-edge neighborhood corona structures based on this parameter.