ABSTRACT

We consider oriented and also signed graphs which are cospectral, i.e. they are not switching isomorphic but share the same spectrum. We prove that there is a bijective correspondence between cospectral bipartite oriented graphs and cospectral bipartite signed graphs. We also give certain constructions of cospectral oriented (signed) graphs; for example, we provide infinite families of cospectral regular signed graphs and cospectral bipartite regular oriented graphs. In particular, we discuss relations between cospectral oriented graphs and cospectral signed graphs.

中文翻译：

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面向共谱图和共谱有符号图

摘要

我们考虑了共谱的定向图和有符号图，即它们没有切换同构，而是共享相同的光谱。我们证明了在共谱二分面向图和共谱二分有向图之间存在双射对应。我们还给出了面向共谱（有符号）图的某些构造。例如，我们提供了无限大的共谱正则符号图和共谱二分正则图。特别地，我们讨论了面向共谱图和共谱有符号图之间的关系。