The signless Laplacian tensor and its H-eigenvalues for an even uniform hypergraph are introduced in this paper. Some fundamental properties of them for an even uniform hypergraph are obtained. In particular, the smal...The signless Laplacian tensor and its H-eigenvalues for an even uniform hypergraph are introduced in this paper. Some fundamental properties of them for an even uniform hypergraph are obtained. In particular, the smallest and the largest H-eigenvalues of the signless Laplacian tensor for an even uniform hypergraph are discussed, and their relationships to hypergraph bipartition, minimum degree, and maximum degree are described. As an application, the bounds of the edge cut and the edge connectivity of the hypergraph involving the smallest and the largest H-eigenvalues are presented.展开更多
We show that a connected uniform hypergraph G is odd-bipartite if and only if G has the same Laplacian and signless Laplacian Z-eigenvalues. We obtain some bounds for the largest （signless） Laplacian Z-eigenvalue of...We show that a connected uniform hypergraph G is odd-bipartite if and only if G has the same Laplacian and signless Laplacian Z-eigenvalues. We obtain some bounds for the largest （signless） Laplacian Z-eigenvalue of a hypergraph. For a k-uniform hyperstar with d edges （2d ≥ k ≥ 3）, we show that its largest （signless） Laplacian Z-eigenvalue is d.展开更多
In this paper,we study the adjacency and signless Laplacian tensors of cored hypergraphs and power hypergraphs.We investigate the properties of their adjacency and signless Laplacian H-eigenvalues.Especially,we find o...In this paper,we study the adjacency and signless Laplacian tensors of cored hypergraphs and power hypergraphs.We investigate the properties of their adjacency and signless Laplacian H-eigenvalues.Especially,we find out the largest H-eigenvalues of adjacency and signless Laplacian tensors for uniform squids.We also compute the H-spectra of sunflowers and some numerical results are reported for the H-spectra.展开更多
We investigate k-uniform loose paths. We show that the largest H- eigenvalues of their adjacency tensors, Laplacian tensors, and signless Laplacian tensors are computable. For a k-uniform loose path with length l≥ 3,...We investigate k-uniform loose paths. We show that the largest H- eigenvalues of their adjacency tensors, Laplacian tensors, and signless Laplacian tensors are computable. For a k-uniform loose path with length l≥ 3, we show that the largest H-eigenvalue of its adjacency tensor is （（1 ＋ √-5）/2）2/k when = 3 and ）λ（A） = 31/k when g = 4, respectively. For the case of l ≥ 5, we tighten the existing upper bound 2. We also show that the largest H-eigenvalue of its signless Laplacian tensor lies in the interval （2, 3） when l≥ 5. Finally, we investigate the largest H-eigenvalue of its Laplacian tensor when k is even and we tighten the upper bound 4.展开更多
文摘The signless Laplacian tensor and its H-eigenvalues for an even uniform hypergraph are introduced in this paper. Some fundamental properties of them for an even uniform hypergraph are obtained. In particular, the smallest and the largest H-eigenvalues of the signless Laplacian tensor for an even uniform hypergraph are discussed, and their relationships to hypergraph bipartition, minimum degree, and maximum degree are described. As an application, the bounds of the edge cut and the edge connectivity of the hypergraph involving the smallest and the largest H-eigenvalues are presented.
基金Supported by National Natural Science Foundation of China(1120140010971029+3 种基金1102606211326045)Talent Youth Teacher Fund of Xinyang Normal UniversityProject for youth teacher of Xinyang Normal University(17(2012))
基金Acknowledgements Foundation of China This work was supported by the National Natural Science （Grant Nos. 11371109, 11426075）, the Natural Science Foundation of tteilongjiang Province （No. QC2014C001）, ：and the Fundamental Research Funds for the Central Universities
文摘We show that a connected uniform hypergraph G is odd-bipartite if and only if G has the same Laplacian and signless Laplacian Z-eigenvalues. We obtain some bounds for the largest （signless） Laplacian Z-eigenvalue of a hypergraph. For a k-uniform hyperstar with d edges （2d ≥ k ≥ 3）, we show that its largest （signless） Laplacian Z-eigenvalue is d.
基金the National Natural Science Foundation of China(No.11271221)the Specialized Research Fund for State Key Laboratories.
文摘In this paper,we study the adjacency and signless Laplacian tensors of cored hypergraphs and power hypergraphs.We investigate the properties of their adjacency and signless Laplacian H-eigenvalues.Especially,we find out the largest H-eigenvalues of adjacency and signless Laplacian tensors for uniform squids.We also compute the H-spectra of sunflowers and some numerical results are reported for the H-spectra.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant No. 11271221） and the Specialized Research Fund for State Key Laboratories.
文摘We investigate k-uniform loose paths. We show that the largest H- eigenvalues of their adjacency tensors, Laplacian tensors, and signless Laplacian tensors are computable. For a k-uniform loose path with length l≥ 3, we show that the largest H-eigenvalue of its adjacency tensor is （（1 ＋ √-5）/2）2/k when = 3 and ）λ（A） = 31/k when g = 4, respectively. For the case of l ≥ 5, we tighten the existing upper bound 2. We also show that the largest H-eigenvalue of its signless Laplacian tensor lies in the interval （2, 3） when l≥ 5. Finally, we investigate the largest H-eigenvalue of its Laplacian tensor when k is even and we tighten the upper bound 4.
