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Moments in graphs
dc.contributor.author | Dalfó Simó, Cristina |
dc.contributor.author | Fiol Mora, Miquel Àngel |
dc.contributor.author | Garriga Valle, Ernest |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV |
dc.date.accessioned | 2013-04-22T10:41:17Z |
dc.date.available | 2013-04-22T10:41:17Z |
dc.date.created | 2013 |
dc.date.issued | 2013 |
dc.identifier.citation | Dalfo, C.; Fiol, M.; Garriga, E. Moments in graphs. "Discrete applied mathematics", 2013, vol. 161, núm. 6, p. 768-777. |
dc.identifier.issn | 0166-218X |
dc.identifier.uri | http://hdl.handle.net/2117/18912 |
dc.description.abstract | Let 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.extent | 10 p. |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs |
dc.subject.lcsh | Graphs, theory of. |
dc.title | Moments in graphs |
dc.type | Article |
dc.subject.lemac | Grafs, Teoria de |
dc.contributor.group | Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions |
dc.rights.access | Open Access |
local.identifier.drac | 11666499 |
dc.description.version | Postprint (author’s final draft) |
local.citation.author | Dalfo, C.; Fiol, M.; Garriga, E. |
local.citation.publicationName | Discrete applied mathematics |
local.citation.volume | 161 |
local.citation.number | 6 |
local.citation.startingPage | 768 |
local.citation.endingPage | 777 |
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