有向超图的超网络能量及其性质

图能量表述为方阵形式的矩阵特征值绝对值之和. 网络能量已在无向图、有向图及混合图中得到较为成功的应用,与传统意义上的图能量之间存在多个相同或相似的上下限. 由于图与超图之间的关联,无向图与有向图的网络能量及无向超图的超网络能量之间存在密切联系. 将超网络能量由无向超图推广应用到有向超图,提出了有向超图的超网络能量,分析了无向超图与有向超图的超网络能量之间的关联,同时论述了无向图与有向图的网络能量及无向超图与有向超图的超网络能量之间的联系,最后给出了有向超图的超网络能量若干重要性质.

Hypernetwork Energy of Directed Hypergraphs and Its Properties

Graph energy is expressed as the sum of all absolute values of eigenvalues of square matrix. Network energies have been applied in undirected graphs,oriented graphs,and mixed graphs successfully,and share several same or similar lower bounds or upper bounds with traditional graph energies. For the relationship between graph and hypergraph,there are closely relationships among network energies of undirected graph and oriented graph and hypernetwork energy of undirected hypergraph. In this paper,the hypernetwork energy of directed hypergraphs is proposed by extended hypernetwork energy from undirected hypergraph to directed hypergraph. The relationship between hypernetwork energies of undirected hypergraph and directed hypergraph is analyzed,and the relationships among network energy of undirected graph and oriented graph and hypernetwork energies of undirected hypergraph and directed hypergraph are also discussed. Finally,several important properties of hypernetwork energy of directed hypergraph are analyzed as well.