The Connected Edge-To-Vertex Geodetic Number of a Graph

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Authors

  • J. John
     Department of Mathematics, Government College of Engineering, Tirunelveli- 627007 ,IN
  • sujitha S.
     Department of Mathematics, Holy Cross College (Autonomous), Nagercoil ,IN

DOI:

https://doi.org/10.18311/jims/2023/26328

Keywords:

Geodesic, Edge-To-Vertex Godetic Number, Connected Edge-To-Vertex Geodetic Number.
05C12.

Abstract

Let G = (V, E) be a graph. A subset S ⊆ E is called an edge-to-vertex geodetic set of G if every vertex of G is either incident with an edge of S or lies on a geodesic joining a pair of edges of S. The minimum cardinality of an edge-to-vertex geodetic set of G is gev(G). Any edge-to-vertex geodetic set of cardinality gev(G) is called an edge-to-vertex geodetic basis of G. A connected edge-to-vertex geodetic set of a graph G is an edge-to-vertex geodetic set S such that the subgraph G[S] induced by S is connected. The minimum cardinality of a connected edge-to-vertex geodetic set of G is the connected edge-to-vertex geodetic number of G and is denoted by gcev(G). Some general properties satisfied by this concept are studied. The connected graphs G of size q with connected edge-to-vertex geodetic number 2 or q or q − 1 are characterized. It is shown that for any three positive integers q, a and b with 2 ≤ a ≤ b ≤ q, there exists a connected graph G of size q, gev(G) = a and gcev(G) = b.

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Published

2023-03-24

How to Cite

John, J., & S., sujitha. (2023). The Connected Edge-To-Vertex Geodetic Number of a Graph. The Journal of the Indian Mathematical Society, 90(1-2), 1–12. https://doi.org/10.18311/jims/2023/26328

Issue

Volume 90, Issue 1-2, January-June 2023

Section

Articles

License

Copyright (c) 2023 J. John, sujitha S.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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Europe PMC
Received 2020-10-30
Accepted 2022-01-23
Published 2023-03-24

 

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