Isomorphism classes and vertex coloring for graphs C[subscript G](a,b)

Abstract

In this thesis, we use the properties of finite abelian group to derive isomorphism testing on the graph C[subscript G](a,b) defined above. We study classes of isomorphic graphs. This work generalizes Nicoloso and Pietropaoli’s paper, which obtain analogous results when is a cyclic group. In addition, we study the algorithms to give an explicit assignment of colors to the vertices of graph C[subscript G](a,b) such that adjacent vertices receive different colors and the number of colors is minimized.