The Distance Spectral Radii of Hypercacti

Abstract

Hypergraphs can model many concepts in computer science, engineering, psychology, etc. The spectral theory is an important research topic, which is widely used in combinatorial mathematics, computer science and social science. This paper mainly concerns the structure of extremal hypergraphs determined by the distance spectral of hypergraphs. A hypercactus is a connected k-uniform hypergraph with any two cycles sharing at most one common vertex. For hypercacti with a fixed number of vertices and cycles, we completely determine the hypercactus structure with minimum distance spectral radius.