Conservative graphs

Abstract

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 K n , for n ≥4, and K 2 n , 2 m , 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.