2-splittable and cordial graphs

Abstract

E. Miller and G. E. Stevens proved in [E. Miller, G. E. Stevens, Some graphs for which even size is sufficient for splittability, Congressus Numerantium 173 (2005), 137–147] the existence of certain families of $2$-splittable caterpillars. In this paper we characterize other families of $2$-splittable caterpillars. Moreover, we show that for some of them there exists a friendly labeling inducing two isomorphic subgraphs.