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A set D of vertices in a graph G is said to be a dominating set of G if every vertex in G is either in D or is adjacent to some vertex in D. Domination number is a graph parameter which is the cardinality of a minimum dominating set of vertices in a graph G. Total, inverse, secure, and secure total domination are variants of the domination parameter. In this paper, we have proved that these parameters are all equal for certain necklace graphs.

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Equality of Domination Parameters in Certain Necklace Graphs

  • 会议论文

  • 发表日期：

    2025年

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  • V. Shalini,
  • Indra Rajasingh

摘要

A set D of vertices in a graph G is said to be a dominating set of G if every vertex in G is either in D or is adjacent to some vertex in D. Domination number is a graph parameter which is the cardinality of a minimum dominating set of vertices in a graph G. Total, inverse, secure, and secure total domination are variants of the domination parameter. In this paper, we have proved that these parameters are all equal for certain necklace graphs.