Some properties on α -least eigenvalue of uniform hypergraphs and their applications

For a connected k -uniform hypergraph H , let 𝒜_α (H)=α𝒟(H)+(1-α )𝒜(H) , where 𝒜(H) (resp. 𝒟(H) ) is its adjacency (resp. degree) tensor and 0≤α <1 . We call the least real eigenvalue of 𝒜_α (H) having a real eigenvector as α -least eigenvalue of H . In this paper, we obtain some properties on α -least eigenvalue of H . As their applications, the extremal hypergraphs whose α -least eigenvalue attaining minimum are characterized among some classes of hypergraphs.