Bibliographic Details
| Title: |
On the Normalized Laplacian Spectrum of the Linear Pentagonal Derivation Chain and Its Application. |
| Authors: |
Zhang, Yuqing1 (AUTHOR) zhangyuqing@stu.xju.edu.cn, Ma, Xiaoling1 (AUTHOR) mathmxl115@xju.edu.cn |
| Superior Title: |
Axioms (2075-1680). Oct2023, Vol. 12 Issue 10, p945. 20p. |
| Subject Terms: |
*SPANNING trees, *LAPLACIAN matrices, *INDEX numbers (Economics) |
| Abstract: |
A novel distance function named resistance distance was introduced on the basis of electrical network theory. The resistance distance between any two vertices u and v in graph G is defined to be the effective resistance between them when unit resistors are placed on every edge of G. The degree-Kirchhoff index of G is the sum of the product of resistance distances and degrees between all pairs of vertices of G. In this article, according to the decomposition theorem for the normalized Laplacian polynomial of the linear pentagonal derivation chain Q P n , the normalize Laplacian spectrum of Q P n is determined. Combining with the relationship between the roots and the coefficients of the characteristic polynomials, the explicit closed-form formulas for degree-Kirchhoff index and the number of spanning trees of Q P n can be obtained, respectively. Moreover, we also obtain the Gutman index of Q P n and we discovery that the degree-Kirchhoff index of Q P n is almost half of its Gutman index. [ABSTRACT FROM AUTHOR] |
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