Cored Hypergraphs, Power Hypergraphs and Their Laplacian H-Eigenvalues

By Shenglong Hu, Liqun Qi, J. Shao. 2013

147 citations recorded by the source corpus.

In this paper, we introduce the class of cored hypergraphs and power hypergraphs, and investigate the properties of their Laplacian H-eigenvalues. From an ordinary graph, one may generate a $k$-uniform hypergraph, called the $k$th power hypergraph of that graph. Power hypergraphs are cored hypergraphs, but not vice versa. Hyperstars, hypercycles, hyperpaths are special cases of power hypergraphs, while sunflowers are a subclass of cored hypergraphs, but not power graphs in general. We show that the largest Laplacian H-eigenvalue of an even-uniform cored hypergraph is equal to its largest signless Laplacian H-eigenvalue. Especially, we find out these largest H-eigenvalues for even-uniform sunflowers. Moreover, we show that the largest Laplacian H-eigenvalue of an odd-uniform sunflower, hypercycle and hyperpath is equal to the maximum degree, i.e., 2. We also compute out the H-spectra of the class of hyperstars. When $k$ is odd, the H-spectra of the hypercycle of size 3 and the hyperpath of length 3 are characterized as well.

Subfields: Computational Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d82e217582d89fefa6c3cd8ad5d818131c33e6d0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mathematics

1. J. Shao
2. Liqun Qi
3. Anirban Banerjee
4. Shenglong Hu
5. Yimin Wei
6. Weiyang Ding
7. Chaoqian Li
8. Yaotang Li

In Geometry and Topology

1. Liqun Qi
2. Anirban Banerjee
3. J. Shao
4. Shenglong Hu
5. Chaoqian Li
6. Yaotang Li

Citations in the corpus

• On the spectrum of hypergraphs (2017, background): “he adjacency matrix of a graph is extended for uniform hypergraphs in [15]. Different properties of eigenvalues of Laplacian and signless Laplacian tensors of a uniform hypergraph have been studied in [20, 21, 22, 34, 35]. Recently Banerjee et al. defined different hypermatrices for non-uniform hypergr”
• M-tensors and nonsingular M-tensors (2013, background): “[7,9,8,15]) is an M-tensor, but is not a nonsingular M-tensor.”
• Some new trace formulas of tensors with applications in spectral hypergraph theory (2013, background): “Also, the cored hypergraphs defined in [9] (every edge contains a vertex of degree one) is a special class of 1-hm bipartite hypergraphs.”