Perfect Equitable Isolate Dominations in Graphs

Authors

  • Mark Caay Polytechnic University of the Philippines
  • Andrew Hernandez Polytechnic University of the Philippines

DOI:

https://doi.org/10.29020/nybg.ejpam.v17i2.4963

Keywords:

perfect domination, equitable domination, perfect equitable domination, isolate domination, perfect equitable isolate domination

Abstract

A subset $S \subseteq V(G)$ is said to be a perfect equitable isolate dominating set of a graph $G$ if it is both perfect equitable dominating set of $G$ and isolate dominating set of $G$. The minimum cardinality of a perfect equitable isolate dominating set is called perfect equitable isolate domination number of $G$ and is denoted by $\gamma_{pe0}(G)$. A perfect equitable isolate dominating set $S$ of $G$ is called $\gamma_{pe0}$-set of $G$. In this paper, the authors give characterizations of a perfect equitable isolate dominating set of some graphs and graphs obtained from the join and corona of two graphs. Furthermore, the perfect equitable isolate domination numbers of these graphs is determined, and the graphs with no perfect equitable isolate dominating sets are investigated.

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Published

2024-04-30

Issue

Section

Nonlinear Analysis

How to Cite

Perfect Equitable Isolate Dominations in Graphs. (2024). European Journal of Pure and Applied Mathematics, 17(2), 969-978. https://doi.org/10.29020/nybg.ejpam.v17i2.4963