1.Institute of Mathematical and Physical Sciences， Hebei GEO University， Shijiazhuang 050031；2.Graduate School， Hebei University of Economics & Business， Shijiazhuang 050061
Abstract：Let k be a nonnegative integer， and G be a graph with p vertices and q edges. The graph G is called to be k-edge-graceful if there exists a bijection f：E→{k，k＋1，k＋2，…，k＋q－1}such that the induced mapping f＋：V→Zp is a bijection too. We denote G is k-edge-graceful. In this paper， the defination is given out which G＝(V，E) is called to be k-edge-graceful graph. And by the especial property of the graph， the necessary condition which the graph S(3，n) is k-edge-graceful is discussed. A method to construct k-edge-graceful graph S(3，n) is given out by recursion and the problem of what sets of natural numbers are the edge-graceful indices of graph S(3，n) is completely resolved when n is even.
刘晓珊,王 琦. S(3，n)的k-边优美的图标号[J]. 华中师范大学学报(自然科学版), 2017, 51(4): 426-428.
LIU Xiaoshan,WANG Qi. On the k-edge-graceful indices of S(3，n). journal1, 2017, 51(4): 426-428.
2017, Vol. 51 
