Moments in graphs
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Inclou dades d'ús des de 2022
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hdl:2117/18912
Tipus de documentArticle
Data publicació2013
Condicions d'accésAccés obert
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continguts d'aquesta obra estan subjectes a la llicència de Creative Commons
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Reconeixement-NoComercial-SenseObraDerivada 3.0 Espanya
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.
CitacióDalfo, C.; Fiol, M.; Garriga, E. Moments in graphs. "Discrete applied mathematics", 2013, vol. 161, núm. 6, p. 768-777.
ISSN0166-218X
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