Limit points for the spectral radii of signed graphs

Abstract

Let Γ=(G,σ) be a signed graph. The spectral radius of Γ is the largest absolute value of its adjacency eigenvalues. In this paper we identify the real numbers which are limit points of spectral radii of signed graphs. This is one of the two aspects of a problem in spectral graph theory known as the Hoffman program, implemented here for signed graphs.