The maximum spectral radius of k-uniform hypergraphs with r pendent vertices

ABSTRACT

Let G be a k-uniform hypergraph. The spectral radius of G is defined as the maximum modulus of eigenvalues of G. In this paper, we characterize the hypergraph on n vertices with maximum spectral radius among all connected k-uniform hypergraphs with exactly r pendent vertices, where $n-r\ge k-3$ or $n-r=1,2$, and establish lower and upper bounds for the maximum spectral radius of connected hypergraphs in terms of the number of pendent vertices when $1\le n-r\le k-1$; We also characterize the unique hypergraphs with maximum spectral radius among all connected k-uniform hypergraphs and supertrees with given number of pendent edges, respectively.

KEYWORDS:

• Spectral radius
• tensor
• pendent vertex
• pendent edge
• power of graphs

AMS SUBJECT CLASSIFICATIONS:

• 05C50
• 05C65
• 15A18

Acknowledgements

The authors would like to thank the anonymous referees for providing constructive comments and help in improving the contents of this paper.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by National Natural Science Foundation of China [No. 11701102]; Natural Science Foundation of Guangdong Province [No. 2017A030313032], [No. 2017A030310441]; the Youth Foundation of Guangdong University of Technology [No. 252151041]; the Scientific research fund of the Science and Technology Program of Guangzhou, China [No. 201510010265].