Zeta-equivalent digraphs: Simultaneous cospectrality

Peter Herbrich

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arXiv · 1412.4763

Zeta-equivalent digraphs: Simultaneous cospectrality

Peter Herbrich

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Abstract

We introduce a zeta function of digraphs that determines, and is determined by, the spectra of all linear combinations of the adjacency matrix, its transpose, the out-degree matrix, and the in-degree matrix. In particular, zeta-equivalence of graphs encompasses simultaneous cospectrality with respect to the adjacency, the Laplacian, the signless Laplacian, and the normalized Laplacian matrix, respectively. In addition, we express zeta-equivalence in terms of Markov chains and in terms of invasions where each edge is replaced by a fixed digraph. We finish with a method for constructing zeta-equivalent digraphs.

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BibTeX RIS

Peter Herbrich. 2014-12-15. Zeta-equivalent digraphs: Simultaneous cospectrality. https://arxiv.org/abs/1412.4763

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