Vol. 22 No. Special Issue (2023): Mapana Journal of Sciences- RECENT DEVELOPMENTS IN PURE AND APPLIED MATHEMATICS
Research Articles

Double Geodetic Number of a Line Graph

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  • Ayarlin Kirupa M.,
  • T. Jebaraj
Ayarlin Kirupa M.
Manonmaniam Sundaranar University, Tirunelveli-627012
T. Jebaraj
Manonmaniam Sundaranar University , Abishekapatti, Tirunelveli-627012, Tamilnadu
DOI: https://doi.org/10.12723/mjs.sp1.3

Published 2023-07-19

Keywords

  • double geodetic number,
  • line graph,
  • cartesian product,
  • vertex covering number

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Abstract

Any line graph L(G), whose vertices correspond to the edges of G(V, E) and two vertices in L(G) are adjacent if and only if the corresponding edges in G are adjacent. If there are vertices u, v in S such that x, y ∈ I[u, v] for any pair of vertices x, y in G, then the set S of vertices of G is said to be a double geodetic set of G. The lowest cardinality of a double geodetic set is represented by the double geodetic number dg(G). In this study, we determine double geodetic number of several line graphs’ double geodetic numbers.

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