Another Look at Hop Independence in Graphs

Authors

  • Jesica Anoche MSU-IIT
  • Sergio Canoy, Jr. MSU-IIT, PRISM

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i1.5658

Keywords:

hop independence number, shadow graph, complementary prism, edge corona, disjunctive product

Abstract

A set $S \subseteq V(G)$ is a hop independent set in an undirected graph $G$ if $d_G(v,w) \ne 2$ for any two distinct vertices $v, w \in S$. The maximum cardinality among the hop independent sets in $G$, denoted by $\alpha_h(G)$, is called the hop independence number of $G$. The hop independent sets in the shadow graph, complementary prism, edge corona and disjunctive products of two graphs are characterized. These characterizations are used to determine the exact or sharp bounds of the hop independence numbers of these graphs. Furthermore, we show that the hop independent set decision problem (HISP) is $NP$-complete. 

Author Biographies

  • Jesica Anoche, MSU-IIT

    Department of Mathematics and Statistics, College of Science and Mathematics, MSU- Iligan Institute of Technology, 9200 Iligan City, Philippines

  • Sergio Canoy, Jr., MSU-IIT, PRISM

    1. Department of Mathematics and Statistics, College of Science and Mathematics, MSU- Iligan Institute of Technology, 9200 Iligan City, Philippines
    2. Center of Mathematical and Theoretical Physical Sciences-PRISM, MSU-Iligan Institute of Technology, 9200 Iligan City, Philippines

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Published

2025-01-31

Issue

Vol. 18 No. 1: (January 2025)

Section

Nonlinear Analysis

License

Copyright (c) 2025 Jesica Anoche, Sergio Canoy, Jr.

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How to Cite

Another Look at Hop Independence in Graphs. (2025). European Journal of Pure and Applied Mathematics, 18(1), 5658. https://doi.org/10.29020/nybg.ejpam.v18i1.5658