Cyclic hypergraphs are the analogue of cyclic graphs. The unicycle hypergraph whose cyclomatic number equals to one is the most elemental cyclic hypergraph. In this paper the maximum size of unicycle hypergraphs is s...Cyclic hypergraphs are the analogue of cyclic graphs. The unicycle hypergraph whose cyclomatic number equals to one is the most elemental cyclic hypergraph. In this paper the maximum size of unicycle hypergraphs is studied. It is proved a piecewise linear function of the order and edge size of the hypergraph.展开更多
For 0≤α<1,theα-spectral radius of an r-uniform hypergraph G is the spectral radius of A_(α)(G)=αD(G)+(1-α)A(G),where D(G)and A(G)are the diagonal tensor of degrees and adjacency tensor of G,respectively.In th...For 0≤α<1,theα-spectral radius of an r-uniform hypergraph G is the spectral radius of A_(α)(G)=αD(G)+(1-α)A(G),where D(G)and A(G)are the diagonal tensor of degrees and adjacency tensor of G,respectively.In this paper,we show the perturbation ofα-spectral radius by contracting an edge.Then we determine the unique unicyclic hypergraph with the maximumα-spectral radius among all r-uniform unicyclic hypergraphs with fixed diameter.We also determine the unique unicyclic hypergraph with the maximumα-spectral radius among all r-uniform unicyclic hypergraphs with given number of pendant edges.展开更多
The spectral radius of a uniform hypergraph is defined to be that of the adjacency tensor of the hypergraph.It is known that the unique unicyclic hypergraph with the largest spectral radius is a nonlinear hypergraph,a...The spectral radius of a uniform hypergraph is defined to be that of the adjacency tensor of the hypergraph.It is known that the unique unicyclic hypergraph with the largest spectral radius is a nonlinear hypergraph,and the unique linear unicyclic hypergraph with the largest spectral radius is a power hypergraph.In this paper we determine the unique linear unicyclic hypergraph with the second or third largest spectral radius,where the former hypergraph is a power hypergraph and the latter hypergraph is a non-power hypergraph.展开更多
文摘Cyclic hypergraphs are the analogue of cyclic graphs. The unicycle hypergraph whose cyclomatic number equals to one is the most elemental cyclic hypergraph. In this paper the maximum size of unicycle hypergraphs is studied. It is proved a piecewise linear function of the order and edge size of the hypergraph.
基金Supported by the National Nature Science Foundation of China(Grant Nos.11871329,11971298)。
文摘For 0≤α<1,theα-spectral radius of an r-uniform hypergraph G is the spectral radius of A_(α)(G)=αD(G)+(1-α)A(G),where D(G)and A(G)are the diagonal tensor of degrees and adjacency tensor of G,respectively.In this paper,we show the perturbation ofα-spectral radius by contracting an edge.Then we determine the unique unicyclic hypergraph with the maximumα-spectral radius among all r-uniform unicyclic hypergraphs with fixed diameter.We also determine the unique unicyclic hypergraph with the maximumα-spectral radius among all r-uniform unicyclic hypergraphs with given number of pendant edges.
基金Natural Science Foundation of China(Grant Nos.11871073,11871077)NSF of Department of Education of Anhui Province(Grant No.KJ2017A362)。
文摘The spectral radius of a uniform hypergraph is defined to be that of the adjacency tensor of the hypergraph.It is known that the unique unicyclic hypergraph with the largest spectral radius is a nonlinear hypergraph,and the unique linear unicyclic hypergraph with the largest spectral radius is a power hypergraph.In this paper we determine the unique linear unicyclic hypergraph with the second or third largest spectral radius,where the former hypergraph is a power hypergraph and the latter hypergraph is a non-power hypergraph.
