Associative spectra of graph algebras are examined with the help of homomorphisms of DFS trees. Undirected graphs are classified according to the associative spectra of their graph algebras; there are only three distinct possibilities: constant 1, powers of 2, and Catalan numbers. Associative and antiassociative digraphs are described, and associative spectra are determined for certain families of digraphs, such as paths, cycles, and graphs on two vertices.

中文翻译：

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图代数I的缔合谱

在DFS树的同态性的帮助下，检查了图代数的缔合谱。无向图根据其图代数的关联光谱进行分类。只有三种不同的可能性：常数1、2的幂和加泰罗尼亚数。描述了关联图和反关联图，并确定了某些图族的关联光谱，例如路径，循环和两个顶点上的图。