Domination number of the non-commuting graph of finite groups
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 vert...
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| Format: | EJournal Article |
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GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB,
2018-10-10.
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| LEADER | 02155 am a22002533u 4500 | ||
|---|---|---|---|
| 001 | EJGTA_284_pdf_78 | ||
| 042 | |a dc | ||
| 100 | 1 | 0 | |a Vatandoost, Ebrahim; Department of Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran |e author |
| 100 | 1 | 0 | |e contributor |
| 700 | 1 | 0 | |a Khalili, Masoumeh; Department of Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran |e author |
| 245 | 0 | 0 | |a Domination number of the non-commuting graph of finite groups |
| 260 | |b GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, |c 2018-10-10. | ||
| 500 | |a https://www.ejgta.org/index.php/ejgta/article/view/284 | ||
| 520 | |a 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 $\gamma(\Gamma_G)<\frac{|G|-|Z(G)|}{2}.$ Also we charactrize all of groups G of order n with t = ∣Z(G)∣, in which $\gamma(\Gamma_{G})+\gamma(\overline{\Gamma}_{G})\in \{n-t+1,n-t,n-t-1,n-t-2\}.$ | ||
| 540 | |a Copyright (c) 2018 Electronic Journal of Graph Theory and Applications (EJGTA) | ||
| 546 | |a eng | ||
| 690 | |a non-commuting graph, dominating set, domination number | ||
| 655 | 7 | |a info:eu-repo/semantics/article |2 local | |
| 655 | 7 | |a info:eu-repo/semantics/publishedVersion |2 local | |
| 655 | 7 | |a Peer-reviewed Article |2 local | |
| 786 | 0 | |n Electronic Journal of Graph Theory and Applications (EJGTA); Vol 6, No 2 (2018): Electronic Journal of Graph Theory and Applications; 228-237 | |
| 786 | 0 | |n 2338-2287 | |
| 787 | 0 | |n https://www.ejgta.org/index.php/ejgta/article/view/284/pdf_78 | |
| 856 | 4 | 1 | |u https://www.ejgta.org/index.php/ejgta/article/view/284/pdf_78 |z Get Fulltext |