Abstract Let Γ be a simple undirected graph on a finite vertex set and let A be its adjacency matrix. Then Γ is singular if A is singular. The problem of characterizing singular graphs is easy to state but very difficult to resolve in any generality. In this paper we investigate the singularity of graphs for which the dihedral group acts transitively on vertices as a group of automorphisms.

中文翻译：

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具有二面体群作用的奇异图

摘要 设Γ 为有限顶点集上的简单无向图，设A 为其邻接矩阵。如果 A 是奇异的，则Γ 是奇异的。表征奇异图的问题很容易表述，但在任何一般情况下都很难解决。在本文中，我们研究了二面体群作为一组自同构在顶点上传递作用的图的奇异性。