On Unitary Cayley Graphs

Abstract

We deal with a family of undirected Cayley graphs $X_n$ which are unions of disjoint Hamilton cycles, and some of their properties, where $n$ runs over the positive integers. It is proved that $X_n$ is a bipartite graph when $n$ is even. If $n$ is an odd number, we count the number of different colored triangles in $X_n$.