In this paper, we defined two classes of hypergraphs, hyperbugs and kite hypergraphs. We show that balanced hyperbugs maximize the spectral radii of hypergraphs with fixed number of vertices and diameter and kite hypergraphs minimize the spectral radii of hypergraphs with fixed number of vertices and clique number.
A supertree is a connected and acyclic hypergraph. Denote by T m , n , α the set of m -uniform supertrees of order n with independent number α . Focusing on the spectral radius in T m , n , α , this present completely determines the hypergraphs with maximum spectral radius among all the supertrees with n vertices and independence number α for m − 1 / m n ≤ α ≤ n − 1 , which extend the results of Lu et al. from tree to uniform supertree. Our techniques are based on the structure properties of supertrees with given independence number and general edge-moving operation. As a byproduct, we also determine the hypergraphs with minimum signless Laplacian spectral radius in T m , n , α .
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