Article Per Year (5 Year)
p-Index From 2020 - 2025
0
P-Index
This Author published in this journals
All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Ebrahim Vatandoost
Department of Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran
Electrical & Electronics Engineering

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

Found 1 Documents
Search

 1 
Domination number of the non-commuting graph of finite groups Ebrahim Vatandoost; Masoumeh Khalili
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 6, No 2 (2018): 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.2018.6.2.3

Abstract

Let G be a non-abelian group. The non-commuting graph of group G, shown by ΓG, is a graph with the vertex set G \ Z(G), where Z(G) is the center of group G. Also two distinct vertices of a and b are adjacent whenever ab ≠ ba. A set S ⊆ V(Γ) of vertices in a graph Γ is a dominating set if every vertex v ∈ V(Γ) is an element of S or adjacent to an element of S. The domination number of a graph Γ denoted by γ(Γ), is the minimum size of a dominating set of Γ. </p><p>Here, we study some properties of the non-commuting graph of some finite groups. In this paper, we show that $\gamma(\Gamma_G)&lt;\frac{|G|-|Z(G)|}{2}.$ Also we charactrize all of groups G of order n with t = ∣Z(G)∣, in which $\gamma(\Gamma_{G})+\gamma(\overline{\Gamma}_{G})\in \{n-t+1,n-t,n-t-1,n-t-2\}.$
Co-Authors Masoumeh Khalili