Fiol, M.; Dalfo, C.; Miller, M.; Ryan, J.; Siran, J.
Type of activity
Presentation of work at congresses
Name of edition
Algebraic and Extremal Graph Theory Conference 2017
Date of publication
2017
Presentation's date
2017-08-10
Book of congress proceedings
Algebraic and Extremal Graph Theory: a conference in honor of W. Haemers, F. Lazebnik, and A. Woldar): Delaware, USA: august 7-10, 2017: book of abstracts
First page
10
Last page
10
Abstract
We study the relationship between two key concepts in the theory of (di)graphs: the quotient digraph, and the lift $\Gamma^\alpha$ of a base (voltage) digraph. These techniques contract or expand a given digraph in order to study its characteristics, or obtain more involved structures.
This study is carried out by introducing a quotient-like matrix, with complex polynomial entries, which fully represents $\Gamma^\alpha$. In particular, such a matrix gives the quotient matrix of a regular partit...
We study the relationship between two key concepts in the theory of (di)graphs: the quotient digraph, and the lift $\Gamma^\alpha$ of a base (voltage) digraph. These techniques contract or expand a given digraph in order to study its characteristics, or obtain more involved structures.
This study is carried out by introducing a quotient-like matrix, with complex polynomial entries, which fully represents $\Gamma^\alpha$. In particular, such a matrix gives the quotient matrix of a regular partition of $\Gamma^\alpha$, and when the involved group is Abelian,
it completely determines the spectrum of $\Gamma^\alpha$.
As some examples of our techniques, we study some basic properties of the Alegre digraph. In addition we completely characterize the spectrum of a new family of digraphs, which contains the generalized Petersen graphs, and that of the Hoffman-Singleton graph.