Sharp Bounds for the Signless Laplacian Spectral Radius of Uniform Hypergraphs

Abstract

Let $$\mathcal {H}$$ be a k-uniform hypergraph on n vertices with degree sequence $$\Delta =d_1 \ge \cdots \ge d_n=\delta $$ . $$E_i$$ denotes the set of edges of $$\mathcal {H}$$ containing i. The average 2-degree of vertex i of $$\mathcal {H}$$ is $$m_i = {\sum \nolimits _{\{ i,i_2 , \ldots i_k \} \in E_i } {d_{i_2 } \ldots d_{i_k } } } / d_i^{k - 1}$$ . In this paper, in terms of $$m_i$$ and $$d_i$$ , we give some upper bounds and lower bounds for the spectral radius of the signless Laplacian tensor ( $$Q(\mathcal {H})$$ ) of $$\mathcal {H}$$ . Some examples are given to show the tightness of these bounds.