Semisymmetric Graphs Defined by Finite-Dimensional Generalized Kac–Moody Algebras
Semisymmetric Graphs Defined by Finite-Dimensional Generalized Kac–Moody Algebras
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DOI：
10.1007/s40840-022-01380-3
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发表时间：
2022-09
影响因子：
1.2
通讯作者：
Fuyuan Yang;Q. Sun;Chao Zhang
中科院分区：
文献类型：
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作者：
Fuyuan Yang;Q. Sun;Chao Zhang
设为有限域，q的幂不是2或3。本文主要阐明有限维广义Kac-Moody代数定义的李图是否为凯莱图。更精确地说，我们证明了图是二面体型群上的Cayley图，Neithernoris顶点传递。此外，是一个哈密尔顿图。作为应用，我们构造了一个无限族的半对称（即，正则、边传递和非顶点传递图）图。
Letbe a finite field withqnot powers of 2 or 3. In this paper, we mainly clarify whether the Lie graph defined by a finite-dimensional generalized Kac–Moody algebra is Cayley graph or not. More precisely, we prove that the graphis a Cayley graph on a group of dihedral type, neithernoris vertex transitive. Moreover,is a Hamiltonian graph. As an application, we construct an infinite family of semisymmetric (i.e., regular, edge-transitive and non-vertex-transitive graphs) graphs.