Signatures, Lifts, and Eigenvalues of Graphs
(2020)
Book Chapter
Liu, S., Peyerimhoff, N., & Vdovina, A. (2020). Signatures, Lifts, and Eigenvalues of Graphs. In F. M. Atay, P. B. Kurasov, & D. Mugnolo (Eds.), Discrete and continuous models in the theory of networks : operator theory : advances and applications (255-269). Birkhäuser Verlag. https://doi.org/10.1007/978-3-030-44097-8_13
We study the spectra of cyclic signatures of finite graphs and the corresponding cyclic lifts. Starting from a bipartite Ramanujan graph, we prove the existence of an infinite tower of 3-cyclic lifts, each of which is again Ramanujan.