A characterization of partially dual graphs
In this article, we extend the recently introduced concept of partially dual ribbon graphs to graphs. We then go on to characterize partial duality of graphs in terms of bijections between edge sets of corresponding graphs. This result generalizes a well-known result of J. Edmonds in which natural duality of graphs is characterized in terms of edge correspondence, and gives a combinatorial characterization of partial duality.  2010 Wiley Periodicals, Inc. J Graph Theory 67: 198-217, 2011
ribbon graphs partial duality duality graphs on surfaces