The spectra of the complements of graphs with given connectivity

Abstract

Spectral radius of a graph $G$ is the largest eigenvalue of adjacency matrix of $G$. The least eigenvalue of a graph $G$ is the least eigenvalue of adjacency matrix of $G$. In this paper we determine the graphs which attain respectively the minimum spectral radius and the minimum least eigenvalue among all complements of connected simple graphs with given connectivity. Spectral radius of a graph $G$ is the largest eigenvalue of adjacency matrix of $G$. The least eigenvalue of a graph $G$ is the least eigenvalue of adjacency matrix of $G$. In this paper we determine the graphs which attain respectively the minimum spectral radius and the minimum least eigenvalue among all complements of connected simple graphs with given connectivity.