On the spectrum 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 Böhmová, 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. Mathematics Subject Classifications: 05C20, 05C50.