Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Lie Theory 27 (2017), No. 1, 139--154Copyright 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 [ Fulltext-pdf  (394  KB)] for subscribers only.