Further results on the expected hitting time, the cover cost and the related invariants of graphs

Huang, Jing; Li, Shuchao; Xie, Zhiyong

doi:10.1016/j.disc.2018.09.019

Cited by 16 publications

(2 citation statements)

References 36 publications

(37 reference statements)

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“…Kemeny's constant, which can be interpreted as the mean number of links the random surfer follows before reaching his destination, is closely related to the effective graph resistance (see References [28, 40 and 41]). It is nice to see that the number of spanning trees and Kemeny's constant of a graph are close to the multiplicative degree‐Kirchhoff index.…”

Section: Introductionmentioning

confidence: 99%

Study on the normalized Laplacian of a penta‐graphene with applications

Zaman

Sun

et al. 2020

Int J of Quantum Chemistry

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Let L n denote a linear pentagonal chain with 2n pentagons. The penta‐graphene (penta‐C), denoted by R n is the graph obtained from L n by identifying the opposite lateral edges in an ordered way, whereas the pentagonal Möbius ring Rn′ is the graph obtained from the L n by identifying the opposite lateral edges in a reversed way. In this paper, through the decomposition theorem of the normalized Laplacian characteristic polynomial and the relationship between its roots and the coefficients, an explicit closed‐form formula of the multiplicative degree‐Kirchhoff index (resp. Kemeny's constant, the number of spanning trees) of R n is obtained. Furthermore, it is interesting to see that the multiplicative degree‐Kirchhoff index of R n is approximately 13 of its Gutman index. Based on our obtained results, all the corresponding results are obtained for Rn′.

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Section: Introductionmentioning

confidence: 99%

Study on the normalized Laplacian of a penta‐graphene with applications

Zaman

Sun

et al. 2020

Int J of Quantum Chemistry

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“…It has been shown [5,7,23] that the escape probability, the first passage time, the cover cost and the commute time of random walks have closely relation with the resistance. For more advances one may be referred to [8,9,11,12] and the references cited in.…”

Section: Introductionmentioning

confidence: 99%

On the resistance distance and Kirchhoff index of a linear hexagonal (cylinder) chain

Huang,

2019

Preprint

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The resistance between two nodes in some resistor networks has been studied extensively by mathematicians and physicists. Let L n be a linear hexagonal chain with n 6-cycles. Then identifying the opposite lateral edges of L n in ordered way yields the linear hexagonal cylinder chain, written as R n . We obtain explicit formulae for the resistance distance r Ln (i, j) (resp. r Rn (i, j)) between any two vertices i and j of L n (resp. R n ).To the best of our knowledge {L n } ∞ n=1 and {R n } ∞ n=1 are two nontrivial families with diameter going to ∞ for which all resistance distances have been explicitly calculated. We determine the maximum and the minimum resistance distances in L n (resp. R n ). The monotonicity and some asymptotic properties of resistance distances in L n and R n are given. As well we give formulae for the Kirchhoff indices of L n and R n respectively.

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