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This study introduces a novel graph coloring approach entitled power dominator sum coloring. The power dominator sum coloring is a proper coloring in which each vertex power dominates all vertices of at least one-color class \(C_1,C_2,C_3,\ldots \) or \(C_k\) , and the total of labels for the colors assigned to all vertices is minimal. In this paper, we have found the strength or chromatic number of power dominator sum coloring, denoted by \(\chi _{pdsum}(G)\) , as well as the chromatic sum denoted by \(\sum _{pdsum}(G)\) for various graphs.

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Power Dominator Sum Coloring of Graphs

  • 会议论文

  • 发表日期：

    2025年

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  • Swati Kharub,
  • Sharmila Mary Arul,
  • Diana Grace Thomas

摘要

This study introduces a novel graph coloring approach entitled power dominator sum coloring. The power dominator sum coloring is a proper coloring in which each vertex power dominates all vertices of at least one-color class \(C_1,C_2,C_3,\ldots \) or \(C_k\) , and the total of labels for the colors assigned to all vertices is minimal. In this paper, we have found the strength or chromatic number of power dominator sum coloring, denoted by \(\chi _{pdsum}(G)\) , as well as the chromatic sum denoted by \(\sum _{pdsum}(G)\) for various graphs.