On the α-Spectral Radius of Uniform Hypergraphs

Abstract

For 0 ≤ α ---lt--- 1 and a uniform hypergraph G, the α-spectral radius of G is the largest H-eigenvalue of αD(G)+(1−α)A(G), where D(G) and A(G) are the diagonal tensor of degrees and the adjacency tensor of G, respectively. We give upper bounds for the α-spectral radius of a uniform hypergraph, propose some transformations that increase the α-spectral radius, and determine the unique hypergraphs with maximum α-spectral radius in some classes of uniform hypergraphs.

Keywords

• α-spectral radius
• α-perron vector
• adjacency tensor
• uniform hypergraph
• extremal hypergraph
• 05c50
• 05c65