On signed graphs whose spectral radius does not exceed $\sqrt{2+\sqrt{5}}$

Abstract

The Hoffman program with respect to any real or complex square matrix M associated to a graph G stems from Hoffman's pioneering work on the limit points for the spectral radius of adjacency matrices of graphs does not exceed 2 + √ 5. A signed graph Ġ = (G, σ) is a pair (G, σ), where G = (V, E) is a simple graph and σ : E(G) → {+1, −1} is the sign function. In this paper, we study the Hoffman program of signed graphs. Here, all signed graphs whose spectral radius does not exceed 2 + √ 5 will be identified.