On the irregularity of uniform hypergraphs

Abstract

Let $H$ be an $r$-uniform hypergraph on $n$ vertices and $m$ edges, and let $d_i$ be the degree of $i\in V(H)$. Denote by $\varepsilon(H)$ the difference of the spectral radius of $H$ and the average degree of $H$. Also, denote \[ s(H)=\sum_{i\in V(H)}\left|d_i-\frac{rm}{n}\right|,~ v(H)=\frac{1}{n}\sum_{i\in V(H)}d_i^{\frac{r}{r-1}}-\left(\frac{rm}{n}\right)^{\frac{r}{r-1}}. \] In this paper, we investigate the irregularity of $r$-uniform hypergraph $H$ with respect to $\varepsilon(H)$, $s(H)$ and $v(H)$, which extend relevant results to uniform hypergraphs.