Conservative graphs
David W. Bange, Anthony E. Barkauskas, Peter J. Slater · Journal of Graph Theory · 1980
Abstract A graph G with q edges is defined to be conservative if the edges of G can be oriented and distinctly numbered with the integers 1, 2,…, q so that at each vertex the sum of the numbers on the inwardly directed edges equals that on the outwardly directed edges. Several classes of graphs, including Kn, for n ≥4, and K2n, 2m, for n, m ≥ 2, are shown to be conservative. It is proven that the dual of a planar graceful graph is conservative, and that the converse of this result is false.