Hop Independent Hop Domination in Graphs

Authors

  • Javier Hassan MSU-Iligan Institute of Technology, 9200, Iligan City, Philippines
  • Sergio Canoy, Jr. MSU-Iligan Institute of Technology

DOI:

https://doi.org/10.29020/nybg.ejpam.v15i4.4577

Keywords:

Hop Independent, Hop Domination

Abstract

Let G be an undirected graph with vertex and edge sets V (G) and E(G), respectively. A set S ⊆ V (G) is called a hop independent hop dominating set of G if S is both hop independent and hop dominating set of G. The minimum cardinality of hop independent hop dominating set of G, denoted by γhih(G), is called the hop independent hop domination number of G. In this paper, we show that the hop independent hop domination number of a graph G lies between the hop domination number and the hop independence number of graph G. We characterize these types of sets in the shadow graph, join, corona, and lexicographic product of two graphs. Moreover, either exact values or bounds of the hop independent hop domination numbers of these graphs are given.

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How to Cite

Hassan, J., & Canoy, Jr., S. (2022). Hop Independent Hop Domination in Graphs. European Journal of Pure and Applied Mathematics, 15(4), 1783–1796. https://doi.org/10.29020/nybg.ejpam.v15i4.4577