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(Referência obtida automaticamente do Web of Science, por meio da informação sobre o financiamento pela FAPESP e o número do processo correspondente, incluída na publicação pelos autores.)

Computational and analytical studies of the Randic index in Erdos-Renyi models

Texto completo
Autor(es):
Martinez-Martinez, C. T. [1, 2] ; Mendez-Bermudez, J. A. [2, 3] ; Rodriguez, Jose M. [4] ; Sigarreta, Jose M. [2, 5]
Número total de Autores: 4
Afiliação do(s) autor(es):
[1] Univ Zaragoza, Inst Biocomputat & Phys Complex Syst BIFI, Zaragoza 50018 - Spain
[2] Benemerita Univ Autonoma Puebla, Inst Fis, Apartado Postal J-48, Puebla 72570 - Mexico
[3] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Dept Matemat Aplicada & Estat, Campus Sao Carlos, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil
[4] Univ Carlos III Madrid, Dept Matemat, Ave Univ 30, Madrid 28911 - Spain
[5] Univ Autonoma Guerrero, Ctr Acapulco, Acapulco De Juarez 39610, Guerrero - Mexico
Número total de Afiliações: 5
Tipo de documento: Artigo Científico
Fonte: Applied Mathematics and Computation; v. 377, JUL 15 2020.
Citações Web of Science: 0
Resumo

In this work we perform computational and analytical studies of the Randi ` c index R(G) in Erdos-Renyi models G(n, p) characterized by n vertices connected independently with probability p is an element of (0, 1). First, from a detailed scaling analysis, we show that <(R) over bar (G)> = < R(G)>/(n/2) scales with the product xi approximate to np, so we can define three regimes: a regime of mostly isolated vertices when xi< 0.01 (R(G) approximate to 0), a transition regime for 0.01 < xi < 10 (where 0 < R(G) < n/2), and a regime of almost complete graphs for xi > 10 (R(G) approximate to n/2). Then, motivated by the scaling of <(R) over bar (G)>, we analytically (i) obtain new relations connecting R(G) with other topological indices and characterize graphs which are extremal with respect to the relations obtained and (ii) apply these results in order to obtain inequalities on R (G) for graphs in Erdos-Renyi models. (C) 2020 Elsevier Inc. All rights reserved. (AU)

Processo FAPESP: 19/06931-2 - Métodos de matrizes aleatórias em redes complexas
Beneficiário:Francisco Aparecido Rodrigues
Linha de fomento: Auxílio à Pesquisa - Pesquisador Visitante - Internacional