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dc.contributor.authorDalfó Simó, Cristina
dc.contributor.authorFiol Mora, Miquel Àngel
dc.contributor.authorGarriga Valle, Ernest
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV
dc.date.accessioned2013-04-22T10:41:17Z
dc.date.available2013-04-22T10:41:17Z
dc.date.created2013
dc.date.issued2013
dc.identifier.citationDalfo, C.; Fiol, M.; Garriga, E. Moments in graphs. "Discrete applied mathematics", 2013, vol. 161, núm. 6, p. 768-777.
dc.identifier.issn0166-218X
dc.identifier.urihttp://hdl.handle.net/2117/18912
dc.description.abstractLet G be a connected graph with vertex set V and a weight function that assigns a nonnegative number to each of its vertices. Then, the -moment of G at vertex u is de ned to be M G(u) = P v2V (v) dist(u; v), where dist( ; ) stands for the distance function. Adding up all these numbers, we obtain the -moment of G: This parameter generalizes, or it is closely related to, some well-known graph invari- ants, such as the Wiener index W(G), when (u) = 1=2 for every u 2 V , and the degree distance D0(G), obtained when (u) = (u), the degree of vertex u. In this paper we derive some exact formulas for computing the -moment of a graph obtained by a general operation called graft product, which can be seen as a generalization of the hierarchical product, in terms of the corresponding -moments of its factors. As a consequence, we provide a method for obtaining nonisomorphic graphs with the same -moment for every (and hence with equal mean distance, Wiener index, degree distance, etc.). In the case when the factors are trees and/or cycles, techniques from linear algebra allow us to give formulas for the degree distance of their product.
dc.format.extent10 p.
dc.language.isoeng
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
dc.subject.lcshGraphs, theory of.
dc.titleMoments in graphs
dc.typeArticle
dc.subject.lemacGrafs, Teoria de
dc.contributor.groupUniversitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions
dc.rights.accessOpen Access
local.identifier.drac11666499
dc.description.versionPostprint (author’s final draft)
local.citation.authorDalfo, C.; Fiol, M.; Garriga, E.
local.citation.publicationNameDiscrete applied mathematics
local.citation.volume161
local.citation.number6
local.citation.startingPage768
local.citation.endingPage777


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