The Normalized Laplacians on Both Two Iterated Constructions Associated with Graph and Their Applications  

作　　者：Chang Liu Yingui Pan Jianping Li Li Dai 

机构地区：[1]College of Liberal Arts and Sciences, National University of Defense Technology, Changsha, China

出　　处：《Journal of Applied Mathematics and Physics》2020年第5期838-860,共23页应用数学与应用物理（英文）

摘　　要：Given a simple connected graph G, we consider two iterated constructions associated with G: Fk (G) and Rk (G) . In this paper, we completely obtain the normalized Laplacian spectrum of Fk (G) and Rk (G) , with k ≥2, respectively. As applications, we derive the closed-formula of the multiplicative degree-Kirchhoff index, the Kemeny’s constant, and the number of spanning trees of Fk?(G)? , Rk?(G) , r-iterative graph ,Frk?(G)? and r-iterative graph , where k?≥2 and r?≥1 . Our results extend those main results proposed by Pan et al. (2018), and we provide a method to characterize the normalized Laplacian spectrum of iteratively constructed complex graphs.Given a simple connected graph G, we consider two iterated constructions associated with G: Fk (G) and Rk (G) . In this paper, we completely obtain the normalized Laplacian spectrum of Fk (G) and Rk (G) , with k ≥2, respectively. As applications, we derive the closed-formula of the multiplicative degree-Kirchhoff index, the Kemeny’s constant, and the number of spanning trees of Fk?(G)? , Rk?(G) , r-iterative graph ,Frk?(G)? and r-iterative graph , where k?≥2 and r?≥1 . Our results extend those main results proposed by Pan et al. (2018), and we provide a method to characterize the normalized Laplacian spectrum of iteratively constructed complex graphs.

关 键 词：Normalized LAPLACIAN MULTIPLICATIVE Degree-Kirchhoff Index Kemeny’s Con-stant SPANNING Tree 

分 类 号：O15[理学—数学]