On mixed almost Moore graphs of diameter two

Mixed almost Moore graphs appear in the context of the Degree/Diameter problem as a class of extremal mixed graphs, in the sense that their order is one less than the Moore bound for mixed graphs. The problem of their existence has been considered before for directed graphs and undirected ones, but...

Descripción completa

Detalles Bibliográficos
Autores: López Lorenzo, Ignacio, Miret, Josep M. (Josep Maria)
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2016
País:España
Institución:Universitat de Lleida (UdL)
Repositorio:Repositori Obert UdL
OAI Identifier:oai:repositori.udl.cat:10459.1/56843
Acceso en línea:http://hdl.handle.net/10459.1/56843
Access Level:acceso abierto
Palabra clave:Degree/Diameter problem
Mixed almost Moore graph
Characteristic polynomial
Cyclotomic polynomial
Permutation cycle structure
Teoria de grafs
Grafs, Teoria de
Descripción
Sumario:Mixed almost Moore graphs appear in the context of the Degree/Diameter problem as a class of extremal mixed graphs, in the sense that their order is one less than the Moore bound for mixed graphs. The problem of their existence has been considered before for directed graphs and undirected ones, but not for the mixed case, which is a kind of generalization. In this paper we give some necessary conditions for the existence of mixed almost Moore graphs of diameter two derived from the factorization in Q[x] of their characteristic polynomial. In this context, we deal with the irreducibility of Φi(x2+x−(r−1)), where Φi(x) denotes the i-th cyclotomic polynomial.