Affiliation:
1. School of Computer, Qinghai Normal University, Xining 810000, China
2. School of Mathematics and Statistics, Qinghai Minzu University, Xining 810000, China
Abstract
The scattering number of a graph G is defined as s(G)=max{ω(G−X)−|X|:X⊂V(G),ω(G−X)>1}, where X is a cut set of G, and ω(G−X) denotes the number of components in G−X, which can be used to measure the vulnerability of network G. In this paper, we generalize this parameter to a hypergraph to measure the vulnerability of uniform hypergraph networks. Firstly, some bounds on the scattering number are given. Secondly, the relations of scattering number between a complete k-uniform hypergraph and complete bipartite k-uniform hypergraph are discussed.
Funder
Natural Science Foundation of Qinghai Province
Reference22 articles.
1. Application of hypergraph theory in chemistry;Konstantinova;Discret. Math.,2001
2. Development of Hypergraph Theory;Wang;J. Comput. Syst. Sci. Int.,2018
3. Hypergraph reconstruction from network data;Young;Commun. Phys.,2021
4. Tough graphs and hamiltonian circuits;Discrete Math.,1973
5. On the edge-toughness of a graph (I);Peng;Southeast Asian Math. Bull.,1988