Bounds for the Kirchhoff Index of Regular Graphs via the Spectra of Their Random Walks

被引：27

作者：

Luis Palacios, Jose ^{[1
]}

Miguel Renom, Jose ^{[1
]}

机构：

[1] Univ Simon Bolivar, Dept Comp Cient & Estadist, Caracas, Venezuela

来源：

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY | 2010年 / 110卷 / 09期

关键词：

hitting times; fundamental matrix; Kemeny's constant; RESISTANCE DISTANCE;

D O I：

10.1002/qua.22323

中图分类号：

O64 [物理化学（理论化学）、化学物理学];

学科分类号：

070304 ; 081704 ;

摘要：

Using probabilistic tools, we give tight upper and lower bounds for the Kirchhoff index of any d-regular N-vertex graph in terms of d, N, and the spectral gap of the transition probability matrix associated to the random walk on the graph. We then use bounds of the spectral gap of more specialized graphs, available in the literature, in order to obtain upper bounds for the Kirchhoff index of these specialized graphs. As a byproduct, we obtain a closed-form formula for the Kirchhoff index of the d-dimensional cube in terms of the first inverse moment of a positive binomial variable. (C) 2009 Wiley Periodicals, Inc. Int J Quantum Chem 110: 1637-1641, 2010

引用

页码：1637 / 1641

页数：5

共 50 条

[31] Analytical results for the distribution of first hitting times of random walks on random regular graphs
Tishby, Ido
Biham, Ofer
Katzav, Eytan
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2021, 54 (14)
[32] Mode-Seeking on Graphs via Random Walks
Cho, Minsu
Lee, Kyoung Mu
2012 IEEE CONFERENCE ON COMPUTER VISION AND PATTERN RECOGNITION (CVPR), 2012, : 606 - 613
[33] Transduction on Directed Graphs via Absorbing Random Walks
De, Jaydeep
Zhang, Xiaowei
Lin, Feng
Cheng, Li
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 2018, 40 (07) : 1770 - 1784
[34] On the Kirchhoff Index of Graphs
Das, Kinkar C.
ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES, 2013, 68 (8-9): : 531 - 538
[35] Walks and regular integral graphs
Stevanovic, Dragan
de Abreu, Nair M. M.
de Freitas, Maria A. A.
Del-Vecchio, Renata
LINEAR ALGEBRA AND ITS APPLICATIONS, 2007, 423 (01) : 119 - 135
[36] Computing Lower Bounds for the Kirchhoff Index Via Majorization Techniques
Clemente, Gian Paolo
Cornaro, Alessandra
MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, 2015, 73 (01) : 175 - 193
[37] Bounds for the Sum-Balaban index and (revised) Szeged index of regular graphs
Lei, Hui
Yang, Hua
APPLIED MATHEMATICS AND COMPUTATION, 2015, 268 : 1259 - 1266
[38] Lower Bounds for the Kirchhoff Index
Li, Rao
MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, 2013, 70 (01) : 163 - 174
[39] Bounds for Kirchhoff index of a graph
Mu, Huijuan
PROCEEDINGS OF THE SEVENTH INTERNATIONAL CONFERENCE OF MATRICES AND OPERATORS (MAO 2012), 2012, : 145 - 148
[40] ON THE 2ND EIGENVALUE AND RANDOM-WALKS IN RANDOM D-REGULAR GRAPHS
FRIEDMAN, J
COMBINATORICA, 1991, 11 (04) : 331 - 362

← 1 2 3 4 5 →