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Geodesic Bipancyclicity Of The Cartesian Product Of Graphs, Amruta V. Shinde, Y.M. Borse
Geodesic Bipancyclicity Of The Cartesian Product Of Graphs, Amruta V. Shinde, Y.M. Borse
Theory and Applications of Graphs
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 …