Strong and Weak Dominating Sets of Graphs Under Some Binary Operations

Authors

  • Jerra Mae Molles MSU IIT AND PRISM
  • Ferdinand Jamil MSU IIT AND PRISM
  • Sergio Canoy Jr MSU IIT AND PRISM

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i4.6851

Keywords:

strong dominating, weak dominating, complementary prism, join, corona, edge corona, lexicographic product

Abstract

A set $S$ of vertices of a graph $G$ is a strong (resp. weak) dominating set of $G$ if for every vertex $v$ of $G$ outside of $S$, there is a vertex $u$ inside of $S$ such that $u$ and $v$ are adjacent and $deg_G(v)\le deg_G(u)$ (resp. $deg_G(v)\ge deg_G(u)$). The minimum cardinality of a strong (resp. weak) dominating set is called the strong (resp. weak) domination number of $G$, and is denoted by $\gamma_s(G)$ (resp. $\gamma_w(G)$). In this paper, we characterize the strong and weak dominating sets of graphs under some binary operations. As a result, we also determine the exact values of or sharp bounds for the corresponding strong and weak domination numbers.

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Published

2025-11-05

Issue

Vol. 18 No. 4: (October 2025)

Section

Discrete Mathematics

License

Copyright (c) 2025 Jerra Mae Molles, Ferdinand Jamil, Sergio Canoy Jr

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How to Cite

Strong and Weak Dominating Sets of Graphs Under Some Binary Operations. (2025). European Journal of Pure and Applied Mathematics, 18(4), 6851. https://doi.org/10.29020/nybg.ejpam.v18i4.6851