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 and Zhongzhi Zhang
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Zixuan Xie: Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai 200433, P. R. China†School of Software, Fudan University, Shanghai 200433, P. R. China
Yucheng Wang: Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai 200433, P. R. China‡School of Computer Science, Fudan University, Shanghai 200433, P. R. China
Wanyue Xu: Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai 200433, P. R. China‡School of Computer Science, Fudan University, Shanghai 200433, P. R. China
Liwang Zhu: Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai 200433, P. R. China‡School of Computer Science, Fudan University, Shanghai 200433, P. R. China
Wei Li: �Academy for Engineering and Technology, Fudan University, Shanghai, 200433, P. R. China
Zhongzhi Zhang: Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai 200433, P. R. China‡School of Computer Science, Fudan University, Shanghai 200433, P. R. China

FRACTALS (fractals), 2023, vol. 31, issue 03, 1-14

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.

Keywords: Simplicial Complex; Pseudo-Fractal; Graph Product; Combinatorial Problem; Domination Number; Independence Number; Chromatic Number; Acyclic Orientations; Perfect Matching; Spanning Trees (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23500226

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