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Title:聽Oriented Cayley graphs with nice eigenvalues

础产蝉迟谤补肠迟:听Let $G$ be a finite abelian group. Bridges and Mena characterized the Cayley graphs on $G$ that have only integer eigenvalues. An oriented Cayley graph on $G$ is a Cayley digraph $X(G,C)$ such that $C$ and $(-C)$ are disjoint. Consider the $(0,1,-1)$ skew-symmetric adjacency matrix of an oriented Cayley graph. We give a characterization of when all its eigenvalues are integer multiples of $sqrt{Delta}$ for some square-free integer $Delta<0$. This also characterizes oriented Cayley graphs on which continuous quantum walks are periodic,聽a necessary condition for the walk to admit uniform mixing or perfect state transfer.聽

Seminar Physique Math茅matique
CRM-Salle 4336-4384, Pav. Andr茅 Aisenstadt