Journal of Lie Theory 27 (2017), No. 1, 139--154
Copyright Heldermann Verlag 2017
Diameters of the Commuting Graphs of Simple Lie Algebras
Dengyin Wang
Dept. of Mathematics, University of Mining and Technology, Xuzhou 221116, P. R. China
wdengyin@126.com
Chunguang Xia
Dept. of Mathematics, University of Mining and Technology, Xuzhou 221116, P. R. China
chgxia@cumt.edu.cn
[Abstract-pdf]
\def\g{{\frak g}} Let $L$ be a Lie algebra with center $Z(L)$. The commuting graph $\Gamma(L)$ of $L$ is a graph with vertex set $L\setminus Z(L)$, two distinct vertices $x$ and $y$ are adjacent if and only if $x$ and $y$ commute, i.e., $[x,y]=0$. Let $\g$ be a finite-dimensional simple Lie algebra over an algebraically closed field of characteristic zero. In this paper, we study the diameter of $\Gamma(\g)$.
Keywords: Lie algebra, commuting graph, diameter.
MSC: 17B, 05C50, 15A27, 15A33, 16P10
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