1.School of Mathematical and Physical Sciences， Hebei GEO University， Shijiazhuang 050031， China；2.School of Mathematics and Statistics， Hebei University of Economics and Business， Shijiazhuang 050061， China
摘要设图G＝(V，E)，其中|V|＝p，|E|＝q.对于k∈N，如果存在一个双射f：E→{k，k＋1，…，k＋q－1}，使得它的导出映射f＋：V→Zp，uMT ExtraaAp(u，v) mod p也是一个双射，则称图G是k-边优美的.对于所有的满足G为k-边优美图的非负整数k构成的集合称为图G的边优美指标集.本文根据轮图的特殊性质，讨论了S(7，n)为k-边优美图的必要条件.根据所得的必要条件，利用递归的方法构造S(7，n)的k-边优美图标号并给出详细证明，从而完全解决了当n为偶数时S(7，n)的边优美指标集问题.
Abstract：Let k be an nonnegative integer， and G be a graph with p vertices and q edges. The graph G is said to be k-edge-graceful if there is a bijection f：E→{k，k＋1，…，k＋q－1}，such that the induced mapping f＋：V→Zp，uMT ExtraaAp(u，v)mod p is a bijection too. In this paper， by the especial property of the graph， the necessary condition which the graph S(7，n) is k-edge-graceful is discussed. A method to construct k-edge-graceful graph S(7，n) is given out by recursion and the problem of what sets of natural numbers are the edge-graceful indices of graph S(7，n) is completely resolved when n is even.
刘晓姗,王 琦. S(7，n)的k-边优美的图标号Z[J]. 华中师范大学学报(自然科学版), 2018, 52(6): 765-767.
LIU Xiaoshan,WANG Qi. On the k-edge-graceful indices of S(7，n). journal1, 2018, 52(6): 765-767.
2018, Vol. 52 
