The smallest spectral radius of bicyclic uniform hypergraphs with a given size

TL;DR

This paper characterizes the bicyclic hypergraphs with the smallest spectral radius for a given size by analyzing a specific iterative sequence related to their spectral properties.

Contribution

It introduces a complete characterization of extremal bicyclic hypergraphs with minimal spectral radius using new sequence analysis and edge operation techniques.

Findings

Identifies the hypergraphs with minimal spectral radius among bicyclic hypergraphs.

Develops a method based on log-concavity of an iteration sequence.

Provides a complete extremal classification for the problem.

Abstract

Identifying graphs with extremal properties is an extensively studied topic in spectral graph theory. In this paper, we study the log-concavity of a type of iteration sequence related to the $\alpha$-normal weighted incidence matrices which is presented by Lu and Man for computing the spectral radius of hypergraphs. By using results obtained about the sequence and the method of some edge operations, we will characterize completely extremal k-graphs with the smallest spectral radius among bicyclic hypergraphs with given size.