Convex Hop Domination in Graphs

Authors

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

DOI:

https://doi.org/10.29020/nybg.ejpam.v16i1.4656

Keywords:

hop domination, convex hop dominating set, 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 convex hop dominating if for every two vertices x, y ∈ C, the vertex set of every x-y geodesic is contained in C and for every v ∈ V (G) \ C, there exists w ∈ C such that dG(v, w) = 2. The minimum cardinality of convex hop dominating set of G, denoted by γconh(G), is called the convex hop domination number of G. In this paper, we show that every two positive integers a and b, where 2 ≤ a ≤ b, are realizable as the connected hop domination number and convex hop domination number, respectively, of a connected graph. We also characterize the convex hop dominating sets in some graphs and determine their convex hop domination numbers.

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Published

2023-01-29

Issue

Section

Nonlinear Analysis

How to Cite

Convex Hop Domination in Graphs. (2023). European Journal of Pure and Applied Mathematics, 16(1), 319-335. https://doi.org/10.29020/nybg.ejpam.v16i1.4656

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