This article is cited in 16 papers

RESEARCH ARTICLE

Power graph of finite abelian groups

T. Tamizh Chelvam, M. Sattanathan

Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli 627 012, Tamil Nadu, India

Abstract: Let $G$ be a group. The power graph $\Gamma_P(G)$ of $G$ is a graph with vertex set $V(\Gamma_P(G)) = G$ and two distinct vertices $x$ and $y$ are adjacent in $\Gamma_P(G)$ if and only if either $x^i=y$ or $y^j=x$, where $2\leq i,j \leq n$. In this paper, we obtain some fundamental characterizations of the power graph. Also, we characterize certain classes of power graphs of finite abelian groups.

Keywords: power graph, planar graph, Eulerian graph, finite group.

MSC: 05C25

Received: 27.10.2011
Revised: 15.07.2012

Language: English

Bibliographic databases:

•