The undirected power graph on the conjugacy classes of a finite group

Articles in Press

Document Type : Original Article

Author

Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran

Abstract

Let

G

be a finite group. The undirected power graph on the conjugacy classes of

G

is the simple graph

P_{C} (G)

whose vertices are the conjugacy classes of

G

and two distinct vertices

C

and

C^{'}

are adjacent if one is a subset of a power of the other. In this paper, we show that the graph

P_{C} (G)

2

-connected whenever either

| π (G) | > 1

Z (G)

is cyclic. Moreover, we classify finite groups

G

whose associated graph

P_{C} (G) - {e}

are bipartite.

Keywords

Main Subjects