@article{Huang2025, 
author = {Da Huang and Xing Chen and Cheng Yan and Zhiyong Yu},
title = {The Laplacian spectra of the RG-join weighted graphs and related asymptotic network indices},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {8},
pages = {18183-18194},
keywords = {networked system, topological index, weighted graph, RG-join, Laplacian spectra, Kirchhoff index},
url = {https://www.sciopen.com/article/10.3934/math.2025810},
doi = {10.3934/math.2025810},
abstract = {In this article, the Laplacian spectra of the RG-join weighted graphs and the related network indices named network coherence, kirchhoff index, and Laplacian-energy-like invariant are studied via algebraic graph theory and analysis approach. First, the Laplacian spectrum of the weighted RG-join graph is derived, then the union of graphs together with the RG-join operation are applied to form the weighted RG-join graphs with several classic substructures, and the mathematical characterizations for the indices are derived by the L-spectra. In addition, the related asymptotic results are also derived. It is found that, based on the RG-join weighted structure, when the cardinalities of all copy sets inner        G    2   are large enough, the network coherence and the Kirchhoff index will be irrelevant with the quantity of copies in        G    2  , and also irrelevant with the edge weight        d    1   in the other subgraph        G    1  .}
}