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JACIII Vol.27 No.4 pp. 554-560
doi: 10.20965/jaciii.2023.p0554
(2023)

Research Paper:

Local Metric Dimension of Certain Classes of Circulant Networks

V. Jude Annie Cynthia* ORCID Icon, M. Ramya*,**, and S. Prabhu*** ORCID Icon

*Department of Mathematics, Stella Maris College
17 Cathedral Road, Chennai, Tamil Nadu 600086, India

**Department of Mathematics, Chevalier T. Thomas Elizabeth College for Women
16 St. Mary’s Road, Maryland, Sembium, Perambur, Chennai, Tamil Nadu 600011, India

***Department of Mathematics, Rajalakshmi Engineering College
Bangalore Highway, Thandalam, Chennai 602105, India

Received:
July 16, 2022
Accepted:
February 28, 2023
Published:
July 20, 2023
Keywords:
local metric basis, local metric dimension, Harary graph, Toeplitz network, ILLIAC network
Abstract

Let G(V,E) be a graph with a set of vertices V and a set of edges E. Then, a minimum subset Wl of V is said to be a local metric basis of G if for any two adjacent vertices u,vVWl there exists a vertex wWl such that d(u,w)d(v,w). The cardinality of a local metric basis is referred to as the local metric dimension of the graph G denoted by βl(G). In this paper, we investigate the local metric dimensions of certain circulant-related architectures such as Harary graphs Hk,n with even k or n, Toeplitz networks, and ILLIAC networks.

Cite this article as:
V. Cynthia, M. Ramya, and S. Prabhu, “Local Metric Dimension of Certain Classes of Circulant Networks,” J. Adv. Comput. Intell. Intell. Inform., Vol.27 No.4, pp. 554-560, 2023.
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