On Harary Spectral Radius with Given Parameters

Abstract

The Harary spectral radius \(\rho(G)\) of a graph \(G\) is the largest eigenvalue of the Harary matrix \(RD(G)\). In this paper, we determine graphs with the largest Harary spectral radius in four classes of simple connected graphs with \(n\) vertices: with given matching number, vertex connectivity, edge connectivity, and chromatic number, respectively.