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

• Published in: International journal of quantum chemistry 2020-05, Vol.120 (9), p.n/a
• Main Authors: Li, Qishun, Zaman, Shahid, Sun, Wanting, Alam, Jawad
• Format: Article
• Language: English
• Subjects: Chemistry; Graph theory; Graphene; multiplicative degree‐Kirchhoff index; normalized Laplacian; penta‐graphene; Physical chemistry; Polynomials; Quantum physics; spanning tree
• ISSN: 0020-7608; 1097-461X
• DOI: 10.1002/qua.26154

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′. The explicit closed‐form formulae for multiplicative degree‐Kirchhoff index, Kemeny's constant and spanning tree number of the pentagraphene and the pentagonal Mobius ring are determined, respectively.