1-Movable Resolving Hop Domination in Graphs

Authors

  • Jerson Mohamad Western Mindanao State University
  • Helen Rara

DOI:

https://doi.org/10.29020/nybg.ejpam.v16i1.4671

Keywords:

1-movable resolving hop dominating set, 1-movable resolving hop domination number, hop dominated superclique, join, corona, lexicographic product

Abstract

Let G be a connected graph. A set W ⊆ V (G) is a resolving hop dominating set of G if W is a resolving set in G and for every vertex v ∈ V (G) \ W there exists u ∈ W such that dG(u, v) = 2. A set S ⊆ V (G) is a 1-movable resolving hop dominating set of G if S is a resolving hop dominating set of G and for every v ∈ S, either S \ {v} is a resolving hop dominating set of G or there exists a vertex u ∈ ((V (G) \ S) ∩ NG(v)) such that (S \ {v}) ∪ {u} is a resolving hop dominating set of G. The 1-movable resolving hop domination number of G, denoted by γ 1 mRh(G) is the smallest cardinality of a 1-movable resolving hop dominating set of G. This paper presents the characterization of the 1-movable resolving hop dominating sets in the join, corona and lexicographic product of graphs. Furthermore, this paper determines the exact value or bounds of their corresponding 1-movable resolving hop domination number.

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Published

2023-01-29

Issue

Section

Nonlinear Analysis

How to Cite

1-Movable Resolving Hop Domination in Graphs. (2023). European Journal of Pure and Applied Mathematics, 16(1), 418-429. https://doi.org/10.29020/nybg.ejpam.v16i1.4671