Signed (0,2)-graphs with few eigenvalues and a symmetric spectrum

Abstract

We investigate properties of signed graphs that have few distinct eigenvalues together with a symmetric spectrum. Our main contribution is to determine all signed rectagraphs (triangle-free signed (Formula presented.) -graphs) with vertex degree at most 6 that have precisely two distinct eigenvalues (Formula presented.). Next, we consider to what extent induced subgraphs of signed graph with two distinct eigenvalues (Formula presented.) are determined by their spectra. Lastly, we classify signed rectagraphs that have a symmetric spectrum with three distinct eigenvalues and give a partial classification for signed (Formula presented.) -graphs with four distinct eigenvalues.