Unicyclic Graphs with Exactly Three Main Eigenvalues

Abstract

In this work, unicyclic graphs with exactly three main Eigen values is studied by using the equitable partition of graphs. By depicting the characteristics of all unicyclic graphs with 3-portion equitable partition, it shows all these unicyclic graphs have exactly three main Eigen values. In addition, the calculation formula of three main Eigen values of these unicyclic graphs is given.