Signed graphs with totally disconnected star complements

Abstract

. We are interested in a signed graph ˙ G which admits a decomposition into a totally disconnected (i.e., without edges) star complement and a signed graph ˙ S induced by the star set. In this study we derive certain properties of ˙ G ; for example, we prove that the number of (distinct) eigenvalues of ˙ S does not exceed the number of those of ˙ G . Some particular cases are also considered.