Strong Regularity of Signed Graphs

Abstract

We introduce the concept of strong regularity for signed graphs, which extends the classical notion of strongly regular graphs by incorporating the effects of edge signs into the combinatorial and spectral framework. Within this setting, every strongly regular graph naturally appears as a special case, corresponding to the all-positive signature. Fundamental properties of strongly regular signed graphs are established, together with construction techniques and relationships to spectral features and structural parameters, including net regularity and walk regularity.