The spectra of subKautz and cyclic Kautz digraphs

Kautz digraphs K(d, `) are a well-known family of dense digraphs, widely studied as a good model for interconnection networks. Closely related with these, the cyclic Kautz CK(d, `) and the subKautz sK(d, 2) digraphs were recently introduced by B¨ohmov´a, Huemer and the author. In this paper we propose a new method to obtain the complete spectra of subKautz sK(d, 2) and cyclic Kautz CK(d, 3) digraphs, for all d ≥ 3, through the HoffmanMcAndrew polynomial and regular partitions. This approach can be useful to find the spectra of other families of digraphs with high regularity. This research is supported by MINECO under project MTM2014-60127-P, and the Catalan Research Council under project 2014SGR1147. This research has also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement No 734922.