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

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.

accepted by Fractals

References in corpus (13)

• Percolation on complex networks: Theory and application
• Abrupt Desynchronization and Extensive Multistability in Globally Coupled Oscillator Simplices
• Fractal and Transfractal Recursive Scale-Free Nets
• Abrupt phase transition of epidemic spreading in simplicial complexes
• Self-similar disk packings as model spatial scale-free networks
• Exact solution for mean first-passage time on a pseudofractal scale-free web
• Recursive graphs with small-world scale-free properties
• Enumeration of spanning trees in a pseudofractal scale-free web
• Exact calculations of first-passage properties on the pseudofractal scale-free web
• Different thresholds of bond percolation in scale-free networks with identical degree sequence
• Domination number and minimum dominating sets in pseudofractal scale-free web and Sierpiński graph
• Contact graphs of disk packings as a model of spatial planar networks
• Coherence Scaling of Noisy Second-Order Scale-Free Consensus Networks