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In 1969, Dewdney introduced the set \(\Gamma\) of \emph{primal graphs}, characterized by the following two properties: every finite, simple graph \(G\) is the union of non-isomorphic, edge-disjoint subgraphs of \(G\) so that each of the subgraphs is in \(\Gamma\); and, if \(G\) is in \(\Gamma\), then the only such union consists of \(G\) itself. In the period around 1990, several works concerning the determination of the graphs in \(\Gamma\) were published and one Ph.D. thesis written. However, the classification of the members of \(\Gamma\) remains elusive. The main point of this work is to simplify and unify some of the principal results of Preen’s Ph.D. thesis that generalize earlier results about primal graphs with maximum degree 2.