Even order uniform hypergraph via the Einstein product

Abstract

AbstractWe propose the algebraic connectivity of an undirected 2m-uniform hypergraph under the Einstein product. We generalize the algebraic connectivity to a directed 2m-uniform hypergraph and reveal the relationship between the vertex connectivity and the algebraic connectivity. We present some results on the eigenvalue multiplicity of the [Formula: see text]-splitting of tensors by the hypergraph method under the Einstein product.

Keywords

• Uniform hypergraph
• the Einstein product
• vertex connectivity
• the algebraic connectivity
• -splitting
• 15A18