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

Author:

Liu Jia-Bao,Wang Kang

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

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