@article{Dai2024, 
author = {Ze-Miao Dai and Jia-Bao Liu and Kang Wang},
title = {Analyzing the normalized Laplacian spectrum and spanning tree of the cross of the derivative of linear networks},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {6},
pages = {14594-14617},
keywords = {(multiplicative degree) Kirchhoff index, Wiener index, Gutman index, spanning trees},
url = {https://www.sciopen.com/article/10.3934/math.2024710},
doi = {10.3934/math.2024710},
abstract = {In this paper, we focus on the strong product of the pentagonal networks. Let        R          n       be a hexagonal network composed of    2  n pentagons and    n quadrilaterals. Let        P          n              2       denote the graph formed by the strong product of        R          n       and its copy        R          n              ′      . By utilizing the decomposition theorem of the normalized Laplacian characteristics polynomial, we characterize the explicit formula of the multiplicative degree-Kirchhoff index completely. Moreover, the complexity of        P          n              2       is determined.}
}