Transit in corona product of graphs

Abstract

The  transit of a vertex $v$ is ``the sum of the lengths of all shortest path with $v$ as an internal vertex'' and the transit index of a graph $G$  is the sum of the transit of all the vertices of it. In this paper we investigate transit of vertices in Corona product of graphs. An expression for transit of vertices in $G_1\circ G_2$, where $G_1$ and $G_2$ are arbitrary is derived. We also compute transit for vertices in $G_1\circ G_2$, in the case where $G_1$ is a path, a cycle, a star, a complete graph and a complete bipartite graph.