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arXiv · 2301.03230

Combinatorial Properties for a Class of Simplicial Complexes Extended from Pseudo-fractal Scale-free Web

Zixuan Xie·Yucheng Wang·Wanyue Xu·Liwang Zhu·Wei Li·Zhongzhi Zhang
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Abstract

Simplicial complexes are a popular tool used to model higher-order interactions between elements of complex social and biological systems. In this paper, we study some combinatorial aspects of a class of simplicial complexes created by a graph product, which is an extension of the pseudo-fractal scale-free web. We determine explicitly the independence number, the domination number, and the chromatic number. Moreover, we derive closed-form expressions for the number of acyclic orientations, the number of root-connected acyclic orientations, the number of spanning trees, as well as the number of perfect matchings for some particular cases.

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Zixuan Xie, Yucheng Wang, Wanyue Xu, Liwang Zhu, Wei Li, Zhongzhi Zhang. 2023-01-09. Combinatorial Properties for a Class of Simplicial Complexes Extended from Pseudo-fractal Scale-free Web. https://doi.org/10.1142/s0218348x23500226

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