
Journal of Lie Theory 27 (2017), No. 1, 139154 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 [Abstractpdf] \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 finitedimensional 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 [ Fulltextpdf (394 KB)] for subscribers only. 