Research Paper:

# Local Metric Dimension of Certain Classes of Circulant Networks

## V. Jude Annie Cynthia^{*}
, M. Ramya^{*,**}, and S. Prabhu^{***}

^{*}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

Let *G(V,E)* be a graph with a set of vertices *V* and a set of edges *E*. Then, a minimum subset *W*_{l} of *V* is said to be a local metric basis of *G* if for any two adjacent vertices *u,v*∈*V*∖*W*_{l} there exists a vertex *w*∈*W*_{l} 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 β_{l}*(G)*. In this paper, we investigate the local metric dimensions of certain circulant-related architectures such as Harary graphs *H*_{k,n} with even *k* or *n*, Toeplitz networks, and ILLIAC networks.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.27 No.4, pp. 554-560, 2023.

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