On the Characterization of a Minimal Resolving Set for Power of Paths

Saha, Laxman, Basak, Mithun, Tiwary, Kalishankar, Das, Kinkar Chandra and Shang, Yilun (2022) On the Characterization of a Minimal Resolving Set for Power of Paths. Mathematics, 10 (14). p. 2445. ISSN 2227-7390

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Official URL: https://doi.org/10.3390/math10142445


For a simple connected graph G=(V,E), an ordered set W⊆V, is called a resolving set of G if for every pair of two distinct vertices u and v, there is an element w in W such that d(u,w)≠d(v,w). A metric basis of G is a resolving set of G with minimum cardinality. The metric dimension of G is the cardinality of a metric basis and it is denoted by β(G). In this article, we determine the metric dimension of power of finite paths and characterize all metric bases for the same.

Item Type: Article
Additional Information: Funding information:: L.S. is supported by the Science and Engineering Research Board, DST, India (Grant No. CRG/2019/006909) and K.C.D. is supported by the National Research Foundation funded by the Korean government (Grant No. 2021R1F1A1050646).
Uncontrolled Keywords: metric dimension, graph, code, resolving set
Subjects: G100 Mathematics
Department: Faculties > Engineering and Environment > Computer and Information Sciences
Depositing User: Rachel Branson
Date Deposited: 13 Jul 2022 13:52
Last Modified: 13 Jul 2022 14:00
URI: http://nrl.northumbria.ac.uk/id/eprint/49545

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