Para acceder a los documentos con el texto completo, por favor, siga el siguiente enlace: http://hdl.handle.net/2117/8048

When almost distance-regularity attains distance-regularity
Dalfó Simó, Cristina; Van Dam, Edwin; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV; Universitat Politècnica de Catalunya. COMBGRAF - Combinatòria, Teoria de Grafs i Aplicacions
Generally speaking, `almost distance-regular graphs' are graphs which share some, but not necessarily all, regularity properties that characterize distance-regular graphs. In this paper we rst propose four basic di erent (but closely related) concepts of almost distance-regularity. In some cases, they coincide with concepts introduced before by other authors, such as walk-regular graphs and partially distance-regular graphs. Here it is always assumed that the diameter D of the graph attains its maximum possible value allowed by its number d+1 of di erent eigenvalues; that is, D = d, as happens in every distance-regular graph. Our study focuses on nding out when almost distance- regularity leads to distance-regularity. In other words, some `economic' (in the sense of minimizing the number of conditions) old and new characterizations of distance- regularity are discussed. For instance, if A0;A1; : : : ;AD and E0;E1; : : : ;Ed denote, respectively, the distance matrices and the idempotents of the graph; and D and A stand for their respective linear spans, any of the two following `dual' conditions su ce: (a) A0;A1;AD 2 A; (b) E0;E1;Ed 2 D. Moreover, other characterizations based on the preintersection parameters, the average intersection numbers and the recurrence coe cients are obtained. In some cases, our results can be also seen as a generalization of the so-called spectral excess theorem for distance-regular graphs.
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
Graph theory
Eigenvalues
Grafs, Teoria de
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/publishedVersion
info:eu-repo/semantics/conferenceObject
         

Mostrar el registro completo del ítem

Documentos relacionados

Otros documentos del mismo autor/a

Dalfó Simó, Cristina; Van Dam, Edwin; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest; Gorissen, Bram
Dalfó Simó, Cristina; Van Dam, Edwin; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Dalfó Simó, Cristina; Van Dam, Edwin; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest; Gorissen, Bram
Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest