Kemeny's constant and the Kirchhoff index for the cluster of highly symmetric graphs

José Luis Palacios; Greg Markowsky

doi:10.1016/j.amc.2021.126283

Kemeny's constant and the Kirchhoff index for the cluster of highly symmetric graphs

José Luis Palacios, Greg Markowsky

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

8 Citations (Scopus)

Abstract

We find closed form formulas for the Kemeny's constant and the Kirchhoff index for the cluster G₁{G₂} of two highly symmetric graphs G₁, G₂, in terms of the parameters of the original graphs. We also discuss some necessary conditions for a graph to be highly symmetric.

Original language	English
Article number	126283
Number of pages	6
Journal	Applied Mathematics and Computation
Volume	406
DOIs	https://doi.org/10.1016/j.amc.2021.126283
Publication status	Published - 1 Oct 2021

Keywords

Electric networks
Highly symmetric graphs
Kemeny constant
Kirchhoff index
Random walks

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10.1016/j.amc.2021.126283

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title = "Kemeny's constant and the Kirchhoff index for the cluster of highly symmetric graphs",

abstract = "We find closed form formulas for the Kemeny's constant and the Kirchhoff index for the cluster G1\{G2\} of two highly symmetric graphs G1, G2, in terms of the parameters of the original graphs. We also discuss some necessary conditions for a graph to be highly symmetric.",

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author = "Palacios, \{Jos{\'e} Luis\} and Greg Markowsky",

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T1 - Kemeny's constant and the Kirchhoff index for the cluster of highly symmetric graphs

AU - Palacios, José Luis

AU - Markowsky, Greg

PY - 2021/10/1

Y1 - 2021/10/1

N2 - We find closed form formulas for the Kemeny's constant and the Kirchhoff index for the cluster G1{G2} of two highly symmetric graphs G1, G2, in terms of the parameters of the original graphs. We also discuss some necessary conditions for a graph to be highly symmetric.

AB - We find closed form formulas for the Kemeny's constant and the Kirchhoff index for the cluster G1{G2} of two highly symmetric graphs G1, G2, in terms of the parameters of the original graphs. We also discuss some necessary conditions for a graph to be highly symmetric.

KW - Electric networks

KW - Highly symmetric graphs

KW - Kemeny constant

KW - Kirchhoff index

KW - Random walks

UR - http://www.scopus.com/inward/record.url?scp=85104722772&partnerID=8YFLogxK

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DO - 10.1016/j.amc.2021.126283

M3 - Article

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SN - 0096-3003

VL - 406

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

M1 - 126283

ER -

Kemeny's constant and the Kirchhoff index for the cluster of highly symmetric graphs

Abstract

Keywords

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