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arXiv · 2007.01300

Integral equienergetic non-isospectral unitary Cayley graphs

Ricardo A. Podestá·Denis E. Videla
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Abstract

We prove that the Cayley graphs $X(G,S)$ and $X^+(G,S)$ are equienergetic for any abelian group $G$ and any symmetric subset $S$. We then focus on the family of unitary Cayley graphs $G_R=X(R,R^*)$, where $R$ is a finite commutative ring with identity. We show that under mild conditions, $\{G_R, G_R^+\}$ are pairs of integral equienergetic non-isospectral graphs (generically connected and non-bipartite). Then, we obtain conditions such that $\{G_R, \bar G_R\}$ are equienergetic non-isospectral graphs. Finally, we characterize all integral equienergetic non-isospectral triples $\{G_R, G_R^+, \bar G_R \}$ such that all the graphs are also Ramanujan.

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Ricardo A. Podestá, Denis E. Videla. 2020-11-30. Integral equienergetic non-isospectral unitary Cayley graphs. https://doi.org/10.1016/j.laa.2020.12.001

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