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Non-Commuting Graphs of Nilpotent Groups |
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| Authors: | Alireza Abdollahi Hamid Shahverdi |
| Affiliation: | 1. Department of Mathematics , University of Isfahan , Isfahan , Iranand School of Mathematics, Institute for Research in Fundamental Science (IPM), Tehran, Irana.abdollahi@math.ui.ac.ir;3. School of Mathematics , Institute for Research in Fundamental Science (IPM) , Tehran , Iran |
| Abstract: | Let G be a non-abelian group and Z(G) be the center of G. The non-commuting graph Γ G associated to G is the graph whose vertex set is G?Z(G) and two distinct elements x, y are adjacent if and only if xy ≠ yx. We prove that if G and H are non-abelian nilpotent groups with irregular isomorphic non-commuting graphs, then |G| = |H|. |
| Keywords: | Graph isomorphism Groups with abelian centralizers Nilpotent groups Non-commuting graph |