Perfect Isolate Domination in Graphs

Authors

  • Cris L. Armada
  • Jamil Hamja MSU-TCTO

DOI:

https://doi.org/10.29020/nybg.ejpam.v16i2.4760

Keywords:

perfect domination number, perfect dominating set, isolate domination number, isolate dominating set, perfect isolate domination number and perfect isolate dominating set

Abstract

Let G = (V (G), E(G)) be a simple connected graph. A set S ⊆ V (G) is said to be a perfect isolate dominating set of G if S is a perfect dominating set and an isolate dominating set of G. The minimum cardinality of a perfect isolate dominating set of G is called perfect isolate domination number, and is denoted by γp0(G). A perfect isolate dominating set S with |S| = γp0(G) is said to be γp0-set. In this paper, the author gives a characterization of perfect isolate dominating set of some graphs and graphs obtained from the join, corona and lexicographic product of two graphs. Moreover, the perfect isolate domination number of the forenamed graphs is determined and also, graphs having no perfect isolate dominating set are examined.

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Published

2023-04-30

Issue

Vol. 16 No. 2: (April 2023)

Section

Nonlinear Analysis

License

Copyright (c) 2023 European Journal of Pure and Applied Mathematics

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How to Cite

Perfect Isolate Domination in Graphs. (2023). European Journal of Pure and Applied Mathematics, 16(2), 1326-1341. https://doi.org/10.29020/nybg.ejpam.v16i2.4760