Decompositions of \(\lambda K_{n}\) into LW and OW Graphs

In this paper, we identify \(LW\) and \(OW\) graphs, find the minimum \(\lambda\) for decomposition of \(\lambda K_n\) into these graphs, and show that for all viable values of \(\lambda\), the necessary conditions are sufficient for \(LW\)- and \(OW\)-decompositions using cyclic decompositions from base graphs.