Computer generation of edge groups and edge colorings of graphs

A computer code and nonnumerical algorithm are developed to construct the edge group of a graph and to enumerate the edge colorings of graphs of chemical interest. The edge colorings of graphs have many applications in nuclear magnetic resonance (NMR), multiple quantum NMR, enumeration of structural isomers of unsaturated organic compounds, and in the construction of configurational integral expansion series in statistical mechanics. The code developed is applied to many NMR graphs, complete graphs containing up to 10 vertices, and the Petersen graph.

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