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Mathematics  2015 

Ordering uniform supertrees by their spectral radii

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Abstract:

A connected and acyclic hypergraph is called a supertree. In this paper we mainly focus on the spectral radii of uniform supertrees. Li, Shao and Qi determined the first two $k$-uniform supertrees with large spectral radii among all the $k$-uniform supertrees on $n$ vertices [H. Li, J. Shao, L. Qi, The extremal spectral radii of $k$-uniform supertrees, arXiv:1405.7257v1, May 2014]. By applying the operation of moving edges on hypergraphs and using the weighted incidence matrix method we extend the above order to the fourth $k$-uniform supertree.

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