On spectral radius of signed graphs without negative even cycles

Abstract

We consider the spectral radius of signed graphs without negative even cycles and its relations with the spectral radius of signed graphs obtained by removing a vertex, removing an edge or reversing the sign of an edge. As an application, we determine signed graphs that maximize the spectral radius in the class of unicyclic signed graphs with fixed order and girth. We also give certain upper bounds on the spectral radius of unicyclic oriented graphs.