Article Per Year (5 Year)
p-Index From 2021 - 2026
0
P-Index
This Author published in this journals
All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Karim Ahmadidelir
Department of Mathematics Tabriz Branch, Islamic Azad University Tabriz, Iran
Electrical & Electronics Engineering

Published : 1 Documents Claim Missing Document
Claim Missing Document
Check
Articles

Found 1 Documents
Search

 1 
Some structural graph properties of the non-commuting graph of a class of finite Moufang loops Hamideh Hasanzadeh Bashir; Karim Ahmadidelir
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 8, No 2 (2020): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2020.8.2.9

Abstract

For any non-abelian group G, the non-commuting graph of G, Γ=ΓG, is a graph with vertex set G \ Z(G), where Z(G) is the set of elements of G that commute with every element of G and distinct non-central elements x and y of G are joined by an edge if and only if xy ≠ yx. This graph is connected for a non-abelian finite group and has received some attention in existing literature. Similarly, the non-commuting graph of a finite Moufang loop has been defined by Ahmadidelir. He has shown that this graph is connected (as for groups) and obtained some results related to the non-commuting graph of a finite non-commutative Moufang loop. In this paper, we show that the multiple complete split-like graphs are perfect (but not chordal) and deduce that the non-commuting graph of Chein loops of the form M(D2n,2) is perfect but not chordal. Then, we show that the non-commuting graph of a non-abelian group G  is split if and only if the non-commuting graph of the Moufang loop M(G,2) is 3-split and then classify all Chein loops that their non-commuting graphs are 3-split. Precisely, we show that for a  non-abelian group G, the non-commuting graph of the Moufang loop M(G,2), is 3-split if and only if G is isomorphic to a Frobenius group of order 2n, n is odd, whose Frobenius kernel is abelian of order n. Finally, we calculate the energy  of  generalized and multiple splite-like graphs, and discuss about the energy and also the number of spanning trees in the case of  the non-commuting graph of  Chein loops of the form M(D2n,2).
Co-Authors Hamideh Hasanzadeh Bashir