Characterizations of regular magic graphs

A graph is magic if the edges can be labeled with nonnegative real numbers such that (i) different edges have distinct labels, and (ii) the sum of the labels of edges incident to each vertex is the same. Regular magic graphs are characterized herein by the nonappearance of certain bipartite subgraphs. This implies that line connectivity is a crucial property for characterizing regular magic graphs and, in fact, bipartite graphs are magic if and only if A(G) 42. With one exceptional class of graphs, nonbipartite graphs are also magic if A(G) 4: 2. A characterization in terms of circuits is given: a graph is magic only when the edges are covered by circuits in a certain pattern.