The $\alpha$-spectral radius of uniform hypergraphs concerning degrees and domination number

Abstract

For $0\le \alpha <1$ and an r-uniform hypergraph H, the $\alpha$-spectral radius of H is the maximum modulus of eigenvalues of $\alpha {\mathcal {D}}(H)+(1-\alpha ){\mathcal {A}}(H)$, where ${\mathcal {D}}(H)$ and ${\mathcal {A}}(H)$ are the diagonal tensor of degrees and the adjacency tensor of H, respectively. In this paper, we give a lower bound on the $\alpha$-spectral radius of a linear r-uniform hypergraph in terms of its domination number. Then, we obtain some bounds on the $\alpha$-spectral radius in terms of vertex degrees and we characterize the extremal hypergraphs attaining the bound.