The Kemeny’s Constant and Spanning Trees of Hexagonal Ring Network

Spanning tree () has an enormous application in computer science and chemistry to determine the geometric and dynamics analysis of compact polymers. In the field of medicines, it is helpful to recognize the epidemiology of hepatitis C virus (HCV) infection. On the other hand, Kemeny’s constant () is...

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Bibliographic Details
Published in:Computers, materials & continua materials & continua, 2022, Vol.73 (3), p.6347-6365
Main Authors: Zaman, Shahid, N. A. Koam, Ali, Al Khabyah, Ali, Ahmad, Ali
Format: Article
Language:English
Subjects:
Computer science
Eigenvalues
Epidemiology
Graph theory
Hepatitis C
Markov analysis
Markov chains
Polynomials
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Summary:Spanning tree () has an enormous application in computer science and chemistry to determine the geometric and dynamics analysis of compact polymers. In the field of medicines, it is helpful to recognize the epidemiology of hepatitis C virus (HCV) infection. On the other hand, Kemeny’s constant () is a beneficial quantifier characterizing the universal average activities of a Markov chain. This network invariant infers the expressions of the expected number of time-steps required to trace a randomly selected terminus state since a fixed beginning state . Levene and Loizou determined that the Kemeny’s constant can also be obtained through eigenvalues. Motivated by Levene and Loizou, we deduced the Kemeny’s constant and the number of spanning trees of hexagonal ring network by their normalized Laplacian eigenvalues and the coefficients of the characteristic polynomial. Based on the achieved results, entirely results are obtained for the Möbius hexagonal ring network.
ISSN:1546-2226
1546-2218
1546-2226
DOI:10.32604/cmc.2022.031958