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Bounds on Co-Independent Liar’s Domination in Graphs

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  • K. Suriya Prabha
  • S. Amutha
  • N. Anbazhagan
  • Ismail Naci Cangul
  • Ghulam Shabbir

Abstract

A set S⊆V of a graph G=V,E is called a co-independent liar’s dominating set of G if (i) for all v∈V, NGv∩S≥2, (ii) for every pair u,v∈V of distinct vertices, NGu∪NGv∩S≥3, and (iii) the induced subgraph of G on V−S has no edge. The minimum cardinality of vertices in such a set is called the co-independent liar’s domination number of G, and it is denoted by γcoiLRG. In this paper, we introduce the concept of co-independent liar’s domination number of the middle graph of some standard graphs such as path and cycle graphs, and we propose some bounds on this new parameter.

Suggested Citation

  • K. Suriya Prabha & S. Amutha & N. Anbazhagan & Ismail Naci Cangul & Ghulam Shabbir, 2021. "Bounds on Co-Independent Liar’s Domination in Graphs," Journal of Mathematics, Hindawi, vol. 2021, pages 1-6, March.
    • Handle: RePEc:hin:jjmath:5544559
    DOI: 10.1155/2021/5544559
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