On Super Edge-graceful Eulerian Graphs

摘要

Let G be a (p,q) graph in which the edges are labeled 1,2,3,...q so that the vertex sums are distinct, mod p, then G is called edge-graceful. J. Mitchem and A. Simoson introduced the concept of super edge-graceful graphs which is a stronger concept than edge-graceful for some classes of graphs. We show here some eulerian graphs are super edge-graceful, but not edge-graceful; and some are edge-graceful but not super edge-graceful. We show that Rosa's type condition for eulerian super edge-graceful graphs does not exist. Moreover, some conjectures are proposed.