Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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PLITHOGENIC VERTEX DOMINATION NUMBER

  • T. BHARATHI (Department of Mathematics, Loyola College, University of Madras) ;
  • S. LEO (Department of Mathematics, Loyola College, University of Madras) ;
  • JEBA SHERLIN MOHAN (Department of Mathematics, Loyola College, University of Madras)
  • Received : 2023.10.11
  • Accepted : 2024.03.19
  • Published : 2024.05.30
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Abstract

The thrust of this paper is to extend the notion of Plithogenic vertex domination to the basic operations in Plithogenic product fuzzy graphs (PPFGs). When the graph is a complete PPFG, Plithogenic vertex domination numbers (PVDNs) of its Plithogenic complement and perfect Plithogenic complement are the same, since the connectivities are the same in both the graphs. Since extra edges are added to the graph in the case of perfect Plithogenic complement, the PVDN of perfect Plithogenic complement is always less than or equal to that of Plithogenic complement, when the graph under consideration is an incomplete PPFG. The maximum and minimum values of the PVDN of the intersection or the union of PPFGs depend upon the attribute values given to P-vertices, the number of attribute values and the connectivities in the corresponding PPFGs. The novelty in this study is the investigation of the variations and the relations between PVDNs in the operations of Plithogenic complement, perfect Plithogenic complement, union and intersection of PPFGs.

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