Ling-Sen Meng

Trees of odd order with at most two vertices of degree two are edge-graceful

A graph G with q edges and p vertices is edge-graceful if some bijection f from E(G) onto {1,...,q} makes the induced vertex sums f^+(v), the sum of f(e) over the edges e incident to v, distinct modulo p. Lee conjectured in 1989 that every tree of odd order is edge-graceful; the broadest general result we have located,...