The effect on the spectral radius of r-graphs by grafting or contracting edges

Abstract

Let ${\mathcal{H}}_n^{(r)}$ be the set of all connected $r$-graphs with given size $n$. In this paper, we investigate the effect on the spectral radius of $r$-uniform hypergraphs by grafting or contracting an edge and then give the ordering of the $r$-graphs with small spectral radius over ${\mathcal{H}}_n^{(r)}$, when $n\ge 20$.