Paper Title
Characteristics of Permutation Graphs using Ambivalent and Non-Ambivalent Conjugacy Classes

Abstract
The aim of this paper is to study special graphs of permutation graphs. In this paper, we introduce two kind of permutation graphs and . The first on based on the number of disjoint cycle factors without the 1-cycle of permutation is given and the second one based on ambivalent and non-ambivalent conjugacy classes in alternating groups. Then we study some of the essential properties of permutation graphs and with their permutations as the vertices and discuss their structures as conjugacy classes in symmetric and alternating groups. In particular, we study the connected permutation graphs and connected permutation components of graph theory. Also, several examples are given to illustrate the concepts introduced in this paper. Keywords: Graph theory, alternating groups, conjugacy classes, permutations, ambivalent groups. AMS Subject Classification (2010): 20E45, 05C25, 20B30.