Geodesic
Diameters of the Commuting Graphs of Simple Lie Algebras
Journal of Lie theory, Tome 27 (2017) no. 1, pp. 139-154
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\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 $\Gamma(\g)$.
Classification : 17B, 05C50, 15A27, 15A33, 16P10
Mots-clés : Lie algebra, commuting graph, diameter 
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     title = {Diameters of the {Commuting} {Graphs} of {Simple} {Lie} {Algebras}},
     journal = {Journal of Lie theory},
     pages = {139--154},
     year = {2017},
     volume = {27},
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D. Wang; C. Xia. Diameters of the Commuting Graphs of Simple Lie Algebras. Journal of Lie theory, Tome 27 (2017) no. 1, pp. 139-154. http://geodesic.mathdoc.fr/item/JLT_2017_27_1_JLT_2017_27_1_a6/