Extremal problems for the p-spectral radius of Berge hypergraphs

Let G be a simple graph. We say that a hypergraph H is a Berge-G if there is a bijection phi: E(G) -> E(H) such that e subset of phi(e) for all e is an element of E(G). For any r-uniform hypergraph H and a real number p >= 1, the p-spectral radius lambda((p)) (H) of H is defined as lambda((p)) (H): = max( parallel to x parallel to p = 1)r Sigma({i1, i2, ..., ir} is an element of E(H) )x(i1) x(i2) ... x(ir). In this paper we study the p-spectral radius of Berge-G (G is an element of C-n(+)) hypergraphs and determine the 3-uniform hypergraphs with maximum p-spectral radius for p >= 1 among all Berge-G (G is an element of C-n(+)) hypergraphs, where C-n(+) is the set of graphs of order n obtained from C-n by adding an edge. (C) 2020 Elsevier Inc. All rights reserved.