On the conjugate graphs of finite p-groups

Graphs can be related to groups by looking at its vertices and edges. The vertices are comprised of the elements or sets from the groups and the edges are the properties and conditions for the graph. Recently, researches on graphs related with groups have attracted many authors. A conjugate graph of a group is defined asits vertex set is the set of non-central classes of G, and two distinct vertices A and B are connected by an edge if and only if they are conjugate. In this research, the conjugacy class of some finite p-groups are first found. Then, the conjugate graphs are determined