## Taiwanese Journal of Mathematics

### Some Properties of the Signless Laplacian and Normalized Laplacian Tensors of General Hypergraphs

#### Abstract

In this paper, we obtain some properties of signless Laplacian eigenvalues of general hypergraphs. We give the upper and the lower bound of edge connectivity of general hypergraphs in terms of average degree, minimum degree, the rank and the number of vertices, or analytic connectivity $\alpha(G)$, respectively. We also give the upper bound of analytic connectivity $\alpha(G)$ of general hypergraphs in terms of the degrees of vertices. Finally, we obtain the bounds of the smallest $H^{+}$-eigenvalue of the normalized Laplacian sub-tensors of general hypergraphs.

#### Article information

Source
Taiwanese J. Math., Volume 24, Number 2 (2020), 265-281.

Dates
Revised: 20 April 2019
Accepted: 23 June 2019
First available in Project Euclid: 2 July 2019

https://projecteuclid.org/euclid.twjm/1562054420

Digital Object Identifier
doi:10.11650/tjm/190606

Mathematical Reviews number (MathSciNet)
MR4078197

Zentralblatt MATH identifier
07192934

#### Citation

Duan, Cunxiang; Wang, Ligong; Li, Xihe. Some Properties of the Signless Laplacian and Normalized Laplacian Tensors of General Hypergraphs. Taiwanese J. Math. 24 (2020), no. 2, 265--281. doi:10.11650/tjm/190606. https://projecteuclid.org/euclid.twjm/1562054420

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