Outer-connected Hop Dominating Sets in Graphs

Authors

  • Chrisley Jade Saromines Mindanao State University - Iligan Institute of Technology
  • Sergio Canoy, Jr. Mindanao State University-Iligan Institute of Technology

DOI:

https://doi.org/10.29020/nybg.ejpam.v15i4.4590

Keywords:

hop domination, outer-connected, join, corona, lexicographic product

Abstract

Let G be an undirected graph with vertex and edge sets V (G) and E(G), respectively. A hop dominating set S ⊆ V (G) is called an outer-connected hop dominating set if S = V (G) or the subgraph ⟨V (G) \ S⟩ induced by V (G) \ S is connected. The minimum size of an outer-connected hop dominating set is the outer-connected hop domination number γfch(G). A dominating set
of size γfch(G) of G is called a γfch-set. In this paper, we investigate the concept and study it for graphs resulting from some binary operations. Specifically, we characterize the outer-connected hop dominating sets in the join, corona and lexicographic products of graphs, and determine bounds of the outer-connected hop domination number of each of these graphs.

Author Biography

Sergio Canoy, Jr., Mindanao State University-Iligan Institute of Technology

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How to Cite

Saromines, C. J., & Canoy, Jr., S. (2022). Outer-connected Hop Dominating Sets in Graphs. European Journal of Pure and Applied Mathematics, 15(4), 1966–1981. https://doi.org/10.29020/nybg.ejpam.v15i4.4590