Analytic connectivity of k-uniform hypergraphs

Abstract

In this paper, we study the analytic connectivity of a k-uniform hypergraph H, denoted by . In addition to computing the analytic connectivity of a complete k-graph, we present several bounds on analytic connectivity that relate it with other graph invariants, such as degree, vertex connectivity, diameter and isoperimetric number.

Keywords:

• H-eigenvalues
• analytic connectivity
• k-uniform hypergraph
• tensor
• bound

AMS Subject Classifications:

• 05C50
• 5A18

Acknowledgements

We would like to thank Professor Liqun Qi for his help and guidance. We also wish to thank the referee for giving several valuable comments and suggestions.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research is supported by the National Natural Science Foundation of China [grant number 11471077], [grant number 31571558].