An equitable partition based construction of graphs with the same spectral radius

Abstract

An equitable partition of a graph is a remarkable tool that provides valuable spectral information. Among other properties, it is known that the spectral radius of the divisor matrix of any equitable partition equals the spectral radius of the graph. Recently, several methods for construction of families of graphs with the same spectral radius emerged in the literature. In this paper, we develop a unified approach to cyclic-graph constructions by formulating a general method for generating families of connected graphs with a common spectral radius, grounded in the theory of equitable partitions.