The Local Resolving Dominating Set of Comb Product Graphs

Reni Umilasari, Liliek Susilowati, Slamin, Savari Prabhu, Osaye J. Fadekemi

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)115-120
Number of pages6
JournalIAENG International Journal of Computer Science
Volume51
Issue number2
Publication statusPublished - Feb 2024

Keywords

  • comb product
  • domination
  • local resolving set
  • metric dimension

Fingerprint

Dive into the research topics of 'The Local Resolving Dominating Set of Comb Product Graphs'. Together they form a unique fingerprint.

Cite this