On the Vertex-Disjoint Paths on Cayley Color Graphs

Abstract

In this paper, we study the strong connectivity of Cayley color graphs when a certain number of vertices are removed. We prove that there are 1/2D1/2 vertex-disjoint paths from every vertex to every other vertex in a Cayley color graph associated with a finite group G and a non redundant generating set D for G. We also extend this result to a certain class of Cayley graphs.