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Abstract <p> For a graph <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\( G\)</EquationSource> </InlineEquation>, a set <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\( S\subseteq V(G) \)</EquationSource> </InlineEquation> is a disjunctive total dominating set if every vertex has a neighbor in <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\( S \)</EquationSource> </InlineEquation> or has at least two vertices in <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\( S \)</EquationSource> </InlineEquation> at distance two from it. The disjunctive total domination number of <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\( G \)</EquationSource> </InlineEquation> is the minimum cardinality of such a set. In this paper, we study disjunctive total domination on the corona and join of graphs. We give some results and establish an upper bound for disjunctive total domination of corona of two graphs. Moreover, we determine the disjunctive total domination number of corona <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\( G\circ H\)</EquationSource> </InlineEquation>, in which <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\( G \)</EquationSource> </InlineEquation> is a star, cycle, complete graph, wheel graph or complete bipartite graph and <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\( H \)</EquationSource> </InlineEquation> is any graph. On the other hand, we determine the disjunctive total domination number of subdivision-vertex and subdivision-edge join of any two graphs. </p>

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Disjunctive Total Domination on the Corona and Join of Graphs

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • C. Çiftçi,
  • A. Aytaç

摘要

Abstract

For a graph \( G\) , a set \( S\subseteq V(G) \) is a disjunctive total dominating set if every vertex has a neighbor in \( S \) or has at least two vertices in \( S \) at distance two from it. The disjunctive total domination number of \( G \) is the minimum cardinality of such a set. In this paper, we study disjunctive total domination on the corona and join of graphs. We give some results and establish an upper bound for disjunctive total domination of corona of two graphs. Moreover, we determine the disjunctive total domination number of corona \( G\circ H\) , in which \( G \) is a star, cycle, complete graph, wheel graph or complete bipartite graph and \( H \) is any graph. On the other hand, we determine the disjunctive total domination number of subdivision-vertex and subdivision-edge join of any two graphs.