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

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arxiv 2301.03230 v1 pith:NHNZ7CYA submitted 2023-01-09 math.CO cs.CG

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 This is my paper
classification math.CO cs.CG
keywords numbercomplexessimplicialacyclicclasscombinatorialorientationspseudo-fractal
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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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