Weakly Convex Hop Dominating Sets in Graphs

Authors

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

DOI:

https://doi.org/10.29020/nybg.ejpam.v16i2.4761

Keywords:

weakly convex hop dominating set, weakly convex hop domination number

Abstract

Let G be an undirected connected graph with vertex and edge sets V (G) and E(G), respectively. A set C ⊆ V (G) is called weakly convex hop dominating if for every two vertices x, y ∈ C, there exists an x-y geodesic P(x, y) such that V (P(x, y)) ⊆ C and for every v ∈ V (G)\C, there exists w ∈ C such that dG(v, w) = 2. The minimum cardinality of a weakly convex hop dominating set of G, denoted by γwconh(G), is called the weakly convex hop domination number of G. In this paper, we introduce and initially investigate the concept of weakly convex hop domination. We show that every two positive integers a and b with 3 ≤ a ≤ b are realizable as the weakly convex hop domination number and convex hop domination number of some connected graph. Furthermore, we characterize the weakly convex hop dominating sets in some graphs under some binary operations.

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Published

2023-04-30

Issue

Section

Nonlinear Analysis

How to Cite

Weakly Convex Hop Dominating Sets in Graphs. (2023). European Journal of Pure and Applied Mathematics, 16(2), 1196-1211. https://doi.org/10.29020/nybg.ejpam.v16i2.4761

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