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Journal of Discrete Mathematical Sciences and Cryptography

(Since 1998)
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Journal of Discrete Mathematical Sciences and Cryptography
Open Access Research Article

Central edge metric dimension of joint graph

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pp. 97–110Vol. 29Issue 1January 2026DOI: 10.47974/JDMSC-2294 Crossmark XML
Received:
20 Nov 2024
Published Online:
20 Nov 2025
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2294
Pages:
97–110

Abstract

Assume that w is a non-trivial connected graph, with u and v representing its vertices and e = uv representing its edges. The shortest total length of the pathways connecting u and v in G is the distance between them, represented by d(u, v). The greatest separation between a vertex u and another vertex in graph G is its eccentricity. The diameter of a graph G is the largest eccentricity among its vertices. Otherwise, the radius of G is equal to the smallest eccentricity. In graph G, a central vertex is the vertex with the least eccentricity. It is feasible to create a distribution path that can reach any location using the concept of central set. The issue of extreme poverty can be resolved if this course is created. In the meantime, the set in which every element is a central vertex is called the central set. Conversely, d(e, w) = mind(u, w), d(v, w) provides the distance between the edge e and the vertex w. In a linked graph G, a set S of the vertex is an edge generating set of G if all the vertices in S distinguish each of two edges in E(G). And then, the least cardinality of an edge generator set of graph G that contains the central set known as the central edge metric dimension, denoted by edimcen (G). In this paper, we investigate edimcen (G) for joint graphs G. 

Keywords

EccentricityCentral setExtreme povertyEdge metric dimensionCentral edge metric dimensionJoint graph

Subject Classifications

05C1205C7505C38

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