Local Metric Dimension of the Line Graph of a Generalized Petersen Graph

Authors

  • Nur Fahri Tadjuddin Universitas Sulawesi Barat

DOI:

https://doi.org/10.30605/proximal.v8i1.4707

Keywords:

Local metric dimension, Line graph, Generalized Petersen Graph

Abstract

Let G be a graph that has a vertex set V(G) and an edge set E(G). Let W={w_1,w_2,…w_k} be a subset of V(G). The representation of a vertex v∈V(G) with respect to W, denoted by r(v|W), is defined as k-vector (d(v,w_1 ),d(v,w_2 ), …, d(v,w_k )). A set W is called a local resolving set of G if r(u│W)≠r(v│W)  for every two adjacent vertices u,v∈V(G). The smallest cardinality of all local resolving set in G is called the local metric dimension of G, denoted by lmd(G). The local resolving set of G with cardinality  lmd⁡(G)  is called a local basis of G. In this paper, we determine the local metric dimension of the line graph of generalized Petersen graph P_(n,1).

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References

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Published

2024-10-21

How to Cite

Tadjuddin, N. F. (2024). Local Metric Dimension of the Line Graph of a Generalized Petersen Graph . Proximal: Jurnal Penelitian Matematika Dan Pendidikan Matematika, 8(1), 12–17. https://doi.org/10.30605/proximal.v8i1.4707

Issue

Vol. 8 No. 1 (2025): Integrasi Matematika, Teknologi, dan Budaya dalam Pendidikan dan Aplikasi Terapan

Section

Articles

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