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Study on the normalized Laplacian of a penta‐graphene with applications
Author(s) -
Li Qishun,
Zaman Shahid,
Sun Wanting,
Alam Jawad
Publication year - 2020
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.26154
Subject(s) - multiplicative function , mathematics , degree (music) , combinatorics , laplace operator , graph , laplacian matrix , resistance distance , discrete mathematics , mathematical analysis , physics , line graph , graph power , acoustics
Let L n denote a linear pentagonal chain with 2 n 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 R n ′ 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 1 3 of its Gutman index. Based on our obtained results, all the corresponding results are obtained for R n ′ .