Vol. 22 No. 4 (2023): Mapana - Journal of Sciences
Research Articles

Changing and Unchanging the Geodetic Number: Edge Removal

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  • G. Micheal Antony Gnana Santhiyagu,
  • S. Balamurugan,
  • R. Arul Ananthan
G. Micheal Antony Gnana Santhiyagu
M. S. University
S. Balamurugan
Manonmaniam Sundaranar University, St Xavier's College
R. Arul Ananthan
Department of Mathematics, St. Xavier’s College (Autonomous), Palayamkottai
DOI: https://doi.org/10.12723/mjs.67.8

Published 2024-03-19

Keywords

  • Geodesic set,
  • Geodetic number

Copyright (c) 2024

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Abstract

Let S be a collection of elements in a vertex set V. If every vertex in a graph G falls on a geodesic connecting two vertices from S, then that graph is said to be a geodesic set. g(G) is the smallest cardinality of the geodesic subset of a graph G is known as the geodetic number. This study investigates how the removal of an edge affects some unique families of graphs' geodetic numbers.

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