2024 : 12 : 8
Sakineh Rahbariyan

Sakineh Rahbariyan

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

Research

Title
On the tree-number of the power graph associated with some finite groups
Type
JournalPaper
Keywords
Power graph , Tree-number, Simple group
Year
2024
Journal AUT Journal of Mathematics and Computing (AJMC)
DOI
Researchers Sakineh Rahbariyan

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 ⟨x⟩ ⊆ ⟨y⟩ or ⟨y⟩ ⊆ ⟨x⟩. Obviously the power graph of any group is always connected, because the identity element of the group is adjacent to all other vertices. We consider κ(G), the number of spanning trees of the power graph associated with a finite group G. In this paper, for a finite group G, first we represent some properties of P(G), then we are going to find some divisors of κ(G), and finally we prove that the simple group A6 ∼= L2(9) is uniquely determined by tree-number of its power graph among all finite simple groups.