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Combinatorial Properties For A Class Of Simplicial Complexes Extended From Pseudo-Fractal Scale-Free Web

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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)

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.

Suggested Citation

  • Zixuan Xie & Yucheng Wang & Wanyue Xu & Liwang Zhu & Wei Li & Zhongzhi Zhang, 2023. "Combinatorial Properties For A Class Of Simplicial Complexes Extended From Pseudo-Fractal Scale-Free Web," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(03), pages 1-14.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:03:n:s0218348x23500226
    DOI: 10.1142/S0218348X23500226
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