The Local Resolving Dominating Set of Comb Product Graphs

The Local Resolving Dominating Set of Comb Product Graphs

The local resolving dominating set studied in this paper is a notion that combines two concepts in graph theory, the local metric dimension and dominations in graphs. Let G and H be connected graphs of orders n and m, respectively; and x a vertex in H hereafter referred to as a linkage vertex. The c...

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Veröffentlicht in:IAENG international journal of computer science 2024-02, Vol.51 (2), p.115
Hauptverfasser: Umilasari, Reni, Susilowati, Liliek, Slamin, Prabhu, Savari, Fadekemi, Osaye J
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Graph theory
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creator Umilasari, Reni
Susilowati, Liliek
Slamin
Prabhu, Savari
Fadekemi, Osaye J
description The local resolving dominating set studied in this paper is a notion that combines two concepts in graph theory, the local metric dimension and dominations in graphs. Let G and H be connected graphs of orders n and m, respectively; and x a vertex in H hereafter referred to as a linkage vertex. The comb product of G and H denoted by G.H, is a graph obtained by taking one copy of G and n copies of H and attaching the i-th copy of H at the vertex x to the i-th vertex of G. In this paper, we determine the local resolving dominating set of the comb products G . Sn with two different linkage vertices, G . Kn, G . Km,n and G . Cm graphs.
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Graph theory
Graphs
title The Local Resolving Dominating Set of Comb Product Graphs
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