LAUSR

Abstract In this paper, we investigate how the adjacency spectral radius and signless Laplacian spectral radius behave when a connected uniform hypergraph is perturbed by grafting edges. We extend the classical theorem of Li and Feng (1979) about spectral radius from connected graphs to connected uniform hypergraphs by using a constructive method. This result also generalizes the results of Cvetkovic and Simic (2009), and Su et al.(2018). As applications, we determine the k-uniform supertrees of order n with the first two smallest adjacency spectral radii (signless Laplacian spectral radii, respectively). Also, we determine the k-uniform supertrees of order n with the first two smallest Laplacian spectral radii, in the case when k is even.