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On Locating-Dominating Set of Regular Graphs

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  • Anuwar Kadir Abdul Gafur
  • Suhadi Wido Saputro
  • Muhammad Kamran Siddiqui

Abstract

Let G be a simple, connected, and finite graph. For every vertex v∈VG, we denote by NGv the set of neighbours of v in G. The locating-dominating number of a graph G is defined as the minimum cardinality of W ⊆ VG such that every two distinct vertices u,v∈VG\W satisfies ∅≠NGu∩W≠NGv∩W≠∅. A graph G is called k-regular graph if every vertex of G is adjacent to k other vertices of G. In this paper, we determine the locating-dominating number of k-regular graph of order n, where k=n−2 or k=n−3.

Suggested Citation

  • Anuwar Kadir Abdul Gafur & Suhadi Wido Saputro & Muhammad Kamran Siddiqui, 2021. "On Locating-Dominating Set of Regular Graphs," Journal of Mathematics, Hindawi, vol. 2021, pages 1-6, September.
    • Handle: RePEc:hin:jjmath:8147514
    DOI: 10.1155/2021/8147514
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