Geodesic bipancyclicity of the Cartesian product of graphs

Authors

Amruta V. Shinde, Savitribai Phule Pune UniversityFollow
Y.M. Borse, Savitribai Phule Pune UNiversityFollow

Publication Date

July 2022

Abstract

A cycle containing a shortest path between two vertices u and v in a graph G is called a (u,v)-geodesic cycle. A connected graph G is geodesic 2-bipancyclic, if every pair of vertices u,v of it is contained in a (u,v)-geodesic cycle of length l for each even integer l satisfying 2d + 2 ≤ l ≤ |V(G)|, where d is the distance between u and v. In this paper, we prove that the Cartesian product of two geodesic hamiltonian graphs is a geodesic 2-bipancyclic graph. As a consequence, we show that for n ≥ 2 every n-dimensional torus is a geodesic 2-bipancyclic graph.

Creative Commons License

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

Recommended Citation

Shinde, Amruta V. and Borse, Y.M. (2022) "Geodesic bipancyclicity of the Cartesian product of graphs," Theory and Applications of Graphs: Vol. 9: Iss. 2, Article 6.
DOI: 10.20429/tag.2022.090206
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol9/iss2/6