Stable Locating-Dominating Sets in the Edge Corona and Lexicographic Product of Graphs

Authors

  • Gina A. Malacas Department of Mathematics and Statistics, College of Science and Mathematics, Center for Graph Theory, Algebra, and Analysis, Premier Research Institute in Science and Mathematics, MSU-Iligan Institute of Technology, Tibanga, Iligan City, Philippines,
  • Sergio Canoy, Jr.
  • Emmy Chacon

DOI:

https://doi.org/10.29020/nybg.ejpam.v16i1.4645

Keywords:

: locating, stable, domination, edge corona, lexicographic product

Abstract

A set S ⊆ V (G) of an undirected graph G is a locating-dominating set of G if for each v ∈ V (G) \ S, there exists w ∈ S such tha vw ∈ E(G) and NG(x) ∩ S ̸= NG(y) ∩ S for any two distinct vertices x and y in V (G) \ S. S is a stable locating-dominating set of G if it is a locating-dominating set of G and S \ {v} is a locating-dominating set of G for each v ∈ S. The minimum cardinality of a stable locating-dominating set of G, denoted by γSLD(G), is called the stable locating-domination number of G. In this paper, we investigate this concept and the corresponding parameter for edge corona and lexicographic product of graphs.

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Published

2023-01-29

Issue

Vol. 16 No. 1: (January 2023)

Section

Nonlinear Analysis

License

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

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How to Cite

Stable Locating-Dominating Sets in the Edge Corona and Lexicographic Product of Graphs. (2023). European Journal of Pure and Applied Mathematics, 16(1), 479-490. https://doi.org/10.29020/nybg.ejpam.v16i1.4645