The multiplicative degree-Kirchhoff index and complexity of a class of linear networks

Jia-Bao Liu; Kang Wang; Jia-Bao Liu; Kang Wang

doi:10.3934/math.2024347

AIMS Mathematics

2024, Volume 9, Issue 3: 7111-7130. doi: 10.3934/math.2024347

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The multiplicative degree-Kirchhoff index and complexity of a class of linear networks

Jia-Bao Liu ^,,
Kang Wang ^,

School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China

Received: 07 December 2023 Revised: 28 January 2024 Accepted: 01 February 2024 Published: 19 February 2024
MSC : 05C50, 05C90

In this paper, we focus on the strong product of the pentagonal networks. Let $ R_{n} $ be a pentagonal 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.
- pentagonal network,
- strong product,
- the normalized Laplacian,
- multiplicative degree-Kirchhoff index,
- complexity
Citation: Jia-Bao Liu, Kang Wang. The multiplicative degree-Kirchhoff index and complexity of a class of linear networks[J]. AIMS Mathematics, 2024, 9(3): 7111-7130. doi: 10.3934/math.2024347

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Abstract

In this paper, we focus on the strong product of the pentagonal networks. Let $ R_{n} $ be a pentagonal 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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