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Study on the normalized Laplacian of a penta‐graphene with applications
International Journal of Quantum Chemistry ( IF 2.3 ) Pub Date : 2020-01-23 , DOI: 10.1002/qua.26154 Qishun Li 1 , Shahid Zaman 2, 3 , Wanting Sun 2 , Jawad Alam 3
International Journal of Quantum Chemistry ( IF 2.3 ) Pub Date : 2020-01-23 , DOI: 10.1002/qua.26154 Qishun Li 1 , Shahid Zaman 2, 3 , Wanting Sun 2 , Jawad Alam 3
Affiliation
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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 
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 
of its Gutman index. Based on our obtained results, all the corresponding results are obtained for 
.
中文翻译：
五石墨烯的标准化拉普拉斯算子及其应用研究
令L n表示具有2 n个五边形的线性五边形链。由R n表示的五石墨烯（penta-C）是从L n通过有序地识别相对的侧边获得的图，而五边形的莫比乌斯环是从L n通过识别相对的侧边获得的图边缘以相反的方式。本文通过归一化拉普拉斯特征多项式的分解定理及其根与系数之间的关系，得出了乘积-Kirchhoff指数的显式闭式公式（分别为Kemeny常数，生成树数）。[R
获得n。此外，有趣的是， R n的乘法度-基尔霍夫指数近似于其古特曼指数。根据我们获得的结果，获得的所有相应结果。
更新日期：2020-03-16
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 of its Gutman index. Based on our obtained results, all the corresponding results are obtained for .
中文翻译：
五石墨烯的标准化拉普拉斯算子及其应用研究
令L n表示具有2 n个五边形的线性五边形链。由R n表示的五石墨烯（penta-C）是从L n通过有序地识别相对的侧边获得的图，而五边形的莫比乌斯环是从L n通过识别相对的侧边获得的图边缘以相反的方式。本文通过归一化拉普拉斯特征多项式的分解定理及其根与系数之间的关系，得出了乘积-Kirchhoff指数的显式闭式公式（分别为Kemeny常数，生成树数）。[R
获得n。此外，有趣的是， R n的乘法度-基尔霍夫指数近似于其古特曼指数。根据我们获得的结果，获得的所有相应结果。
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