Combinatorial Properties for a Class of Simplicial Complexes Extended from Pseudo-fractal Scale-free Web
arXiv:2301.03230 · doi:10.1142/S0218348X23500226
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.
arXiv commentaccepted by Fractals
References in corpus (31)
- Emergence of scaling in random networks
- The structure and function of complex networks
- Higher-order organization of complex networks
- Simplicial models of social contagion
- Control Principles of Complex Networks
- Evolutionary dynamics of higher-order interactions in social networks
- Simplicial Closure and higher-order link prediction
- Pseudofractal Scale-free Web
- Clique topology reveals intrinsic geometric structure in neural correlations
- 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
- Simplicial Activity Driven Model
- Simplicial complexes and complex systems
- Inverted Berezinskii-Kosterlitz-Thouless Singularity and High-Temperature Algebraic Order in an Ising Model on a Scale-Free Hierarchical-Lattice Small-World Network
- 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
- Weighted Growing Simplicial Complexes
- Random Walks on deterministic Scale-Free networks: Exact results
- Growing scale-free simplices
- Enumeration of spanning trees in a pseudofractal scale-free web
- A general geometric growth model for pseudofractal scale-free web
- Topological Percolation on Hyperbolic Simplicial Complexes
- 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
- Spanning Trees of Recursive Scale-Free Graphs