Uniformly resolvable $(C_4, K_{1,3})$-designs of order $v$ and index $2$

Abstract

In this paper we consider the uniformly resolvable decompositions of the complete graph $2K_v$ into subgraphs where each resolution class contains only blocks isomorphic to the same graph. We completely determine the spectrum for the cases in which all the resolution classes are either $C_4$ or $K_{1,3}$.