Research On Estrada Index Of Several General Linear Hypergraphs

Since Estrada introduced the Estrada index in the ordinary graph in 2000,it has been found that the Estrada index has played an important role in various fields.Hypergraph is a natural generalization of ordinary graphs.Compared with ordinary graphs,hypergraph models can better reflect the relationship between complex and multi-objective objects in reality.Therefore,it is also of great significance to study the Estrada index of hypergraph.But so far,there are fewer research results about the Estrada index of hypergraphs.In this paper,three types of hypergraphs with extreme value of Estrada index in general linear hypergraphs are given.The main results are as follows:The first type,we give the hypergraph with maximum Estrada index in the general hypertree set.The second type,the hypergraph with minimum Estrada index in the linear hyperpath set with fixed vertices and fixed hyperedges is given.The third type,the hypergraphs with maximum and minimum Estrada indices in the set of k-uniform linear unicyclic hypergraphs are given.