Induced Geodetic Sequence of a Graph

Document Type : Research Paper

Authors

1 Department of Mathematics, Bishop Chulaparambil Memorial(BCM) College, Kottayam - 686001

2 Department of Mathematics, Bishop Chulaparambil Memorial(BCM) College, Kottayam, Kerala, India

10.22108/toc.2024.138982.2100

Abstract

A vertex subset $S$ of a graph $G=(V,E)$ is said to be a geodetic set if every vertex in $G$ is in some $u-v$ geodesic for any $u,v \in S$. The minimum cardinality of such a set is the geodetic number, which is denoted as $g(G)$. In this paper, we introduce the concepts of induced geodetic number and induced geodetic sequence of a graph. We discuss this concept in some graph classes. Also, established the characterization of induced geodetic sequences for trees, unicyclic graphs and cacti.

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References

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Transactions on Combinatorics

Articles in Press, Corrected Proof
Available Online from 17 September 2024

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History

  • Receive Date: 01 September 2023
  • Revise Date: 22 July 2024
  • Accept Date: 22 July 2024
  • Published Online: 17 September 2024

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