Simply sequential and graceful graphs
David W. Bange, Anthony E. Barkauskas, Peter J. Slater · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 1979
The concept of a simply sequential graph is introduced as follows. A graph G with V(G) U E(G) = k is called simply sequential if there is a bijection h:V(G) U E(G) ..-->.. (1,2...,k) such that for each edge e = xy in E(G) one has h(e) = h(x) - h(y). Several problems concerning graceful and simply sequential graphs are discussed. In particular, it is conjectured that all trees are simply sequential. 5 figures.