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Sakineh Rahbariyan

Sakineh Rahbariyan

Academic rank: Assistant Professor
ORCID: https://orcid.org/0000-0001-7193-3850
Education: PhD.
ScopusId: 52364509200
Faculty: Science
Address: Arak University
Phone:

Research

Title
On the power graph associated with a group
Type
Presentation
Keywords
Power graph; spectrum; strongly regular graph; planar graph; bipartite graph; cut-edge.
Year
2012
Researchers Sakineh Rahbariyan

Abstract

The power graph P(G) of a group G is a simple graph whose vertex-set is G and two vertices x and y in G are adjacent if and only if one of them is a power of the other. The subgraph P∗(G) of P(G) is obtained by deleting the vertex 1 (the identity element of G). In this paper, we first investigate some properties of the power graph P(G) and its subgraph P∗(G). We next provide necessary and sufficient conditions for a power graph P∗(G) to be a strongly regular graph, a bipartite graph or a planar graph. Finally, we obtain some infinite families of finite groups G for which the power graph P∗(G) contains some cut-edges.