6 research outputs found
A new general family of mixed graphs
A new general family of mixed graphs is presented, which generalizes both the pancake graphs and the cycle prefix digraphs. The obtained graphs are vertex transitive and, for some values of the parameters, they constitute the best infinite families with asymptotically optimal (or quasi-optimal) diameter for their number of verticesPeer ReviewedPostprint (author's final draft
Spectra and eigenspaces from regular partitions of Cayley (di)graphs of permutation groups
In this paper, we present a method to obtain regular (or equitable)
partitions of Cayley (di)graphs (that is, graphs, digraphs, or mixed graphs) of
permutation groups on letters. We prove that every partition of the number
gives rise to a regular partition of the Cayley graph. By using
representation theory, we also obtain the complete spectra and the eigenspaces
of the corresponding quotient (di)graphs. More precisely, we provide a method
to find all the eigenvalues and eigenvectors of such (di)graphs, based on their
irreducible representations. As examples, we apply this method to the pancake
graphs and to a recent known family of mixed graphs
(having edges with and without direction). As a byproduct, the existence of
perfect codes in allows us to give a lower bound for the multiplicity of
its eigenvalue