Computing the Laplacian spectrum and Wiener index of pentagonal-derivation cylinder/Möbius network

Ali, Umar; Li, Junxiang; Ahmad, Yasir; Raza, Zahid

doi:10.1016/j.heliyon.2024.e24182

Cited by 1 publication

(1 citation statement)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this article, motivated by previous works [26][27][28], we establish some explicit closedform formulae for the GMFPT and Kemeny constant in the context of spiro-ring networks, using the Laplacian decomposition theorem. On the basis of the obtained results, comparative studies are carried out for them.…”

Section: Notation and Definitionsmentioning

confidence: 99%

Study of Random Walk Invariants for Spiro-Ring Network Based on Laplacian Matrices

Ahmad,

Ali,

Otera

et al. 2024

Mathematics

Self Cite

View full text Add to dashboard Cite

The use of the global mean first-passage time (GMFPT) in random walks on networks has been widely explored in the field of statistical physics, both in theory and practical applications. The GMFPT is the estimated interval of time needed to reach a state j in a system from a starting state i. In contrast, there exists an intrinsic measure for a stochastic process, known as Kemeny’s constant, which is independent of the initial state. In the literature, it has been used as a measure of network efficiency. This article deals with a graph-spectrum-based method for finding both the GMFPT and Kemeny’s constant of random walks on spiro-ring networks (that are organic compounds with a particular graph structure). Furthermore, we calculate the Laplacian matrix for some specific spiro-ring networks using the decomposition theorem of Laplacian polynomials. Moreover, using the coefficients and roots of the resulting matrices, we establish some formulae for both GMFPT and Kemeny’s constant in these spiro-ring networks.

show abstract

Section: Notation and Definitionsmentioning

confidence: 99%