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

Abstract

AbstractWe 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 ‐graphs) with vertex degree at most 6 that have precisely two distinct eigenvalues . Next, we consider to what extent induced subgraphs of signed graph with two distinct eigenvalues 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 ‐graphs with four distinct eigenvalues.