Some bounds on the eigenvalues of uniform hypergraphs

Abstract

Let $\mathcal{H}$ be a uniform hypergraph. Let $\mathcal{A}(\mathcal{H})$ and $\mathcal{Q}(\mathcal{H})$ be the adjacency tensor and the signless Laplacian tensor of $\mathcal{H}$, respectively. In this note we prove several bounds for the spectral radius of $\mathcal{A}(\mathcal{H})$ and $\mathcal{Q}(\mathcal{H})$ in terms of the degrees of vertices of $\mathcal{H}.$