Analyzing the normalized Laplacian spectrum and spanning tree of the cross of the derivative of linear networks

Autor: Ze-Miao Dai, Jia-Bao Liu, Kang Wang
Jazyk: angličtina
Rok vydání: 2024
Předmět:
Zdroj: AIMS Mathematics, Vol 9, Iss 6, Pp 14594-14617 (2024)
Druh dokumentu: article
ISSN: 2473-6988
DOI: 10.3934/math.2024710?viewType=HTML
Popis: In this paper, we focus on the strong product of the pentagonal networks. Let $ R_{n} $ be a hexagonal network composed of $ 2n $ pentagons and $ n $ quadrilaterals. Let $ P_{n}^{2} $ denote the graph formed by the strong product of $ R_{n} $ and its copy $ R_{n}^{\prime} $. 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.
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