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We investigate properties of signed graphs that have few distinct eigenvaluestogether with a symmetric spectrum. Our main contribution is to determine allsigned $(0,2)$-graphs with vertex degree at most $6$ that have precisely twodistinct eigenvalues $\pm \lambda$. Next, we consider to what extent inducedsubgraphs of signed graph with two distinct eigenvalues $\pm \lambda$ aredetermined by their spectra. Lastly, we classify signed $(0,2)$-graphs thathave a symmetric spectrum with three distinct eigenvalues and give a partialclassification for those with four distinct eigenvalues.

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