An overview of the degree/diameter problem for directed, undirected and mixed graphs
Visualitza/Obre
Estadístiques de LA Referencia / Recolecta
Inclou dades d'ús des de 2022
Cita com:
hdl:2099/10382
Tipus de documentText en actes de congrés
Data publicació2011
EditorIniciativa Digital Politècnica
Condicions d'accésAccés obert
Tots els drets reservats. Aquesta obra està protegida pels drets de propietat intel·lectual i
industrial corresponents. Sense perjudici de les exempcions legals existents, queda prohibida la seva
reproducció, distribució, comunicació pública o transformació sense l'autorització del titular dels drets
Abstract
A well-known fundamental problem in extremal graph theory is the degree/diameter problem, which is to determine the largest (in terms of the number of vertices) graphs or digraphs or mixed graphs of given maximum degree, respectively, maximum outdegree,
respectively, mixed degree; and given diameter. General upper bounds, called Moore bounds, exist for the largest possible
order of such graphs, digraphs and mixed graphs of given maximum degree d (respectively, maximum out-degree d, respectively, maximum mixed degree) and diameter k.
In recent years, there have been many interesting new results in all these three versions of the problem, resulting in improvements in both the lower bounds and the upper bounds on the largest possible number of vertices. However, quite a number of questions regarding the degree/diameter problem are still wide open. In this paper we present an overview of the current state
of the degree/diameter problem, for undirected, directed and mixed graphs, and we outline several related open problems.
CitacióMiller, Mirka. An overview of the degree/diameter problem for directed, undirected and mixed graphs. A: International Workshop on Optimal Networks Topologies. "Proceedings of the 3rd International Workshop on Optimal Networks Topologies IWONT 2010". Barcelona: Iniciativa Digital Politècnica, 2011, p. 335-345.
ISBN978-84-7653-565-3
Col·leccions
Fitxers | Descripció | Mida | Format | Visualitza |
---|---|---|---|---|
335_miller_overview_degree_diameter.pdf | 554,4Kb | Visualitza/Obre |