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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
\The number of spanning trees of power graphs associated with speci c groups and some applications"
Type
JournalPaper
Keywords
power graph, group, tree-number.
Year
2017
Journal ARS COMBINATORIA
DOI
Researchers Alireza moghadamfar ، Sakineh Rahbariyan ، S. Navid Salehy ، S. Nima Salehy

Abstract

Given a group G, we define the power graph P(G) as follows: the vertices are the elements of G and two vertices x and y are joined by an edge if hxi  hyi or hyi  hxi. Obviously the power graph of any group is always connected, because the identity element of the group is adjacent to all other vertices. In the present paper, among other results, we will find the number of spanning trees of the power graph associated with specific finite groups. We also determine, up to isomorphism, the structure of a finite group G whose power graph has exactly n spanning trees, for n < 53. Finally, we show that the alternating group A5 is uniquely determined by tree-number of its power graph among all finite simple groups