S(3,n)的k-边优美的图标号  

On the k-edge-graceful indices of S(3,n)

作　　者：刘晓珊 王琦[2] LIU Xiaoshan WANG Qi(Institute of Mathematical and Physical Sciences, Hebei GEO University, Shijiazhuang 050031 Graduate School, Hebei University of Economics ＆ Business, Shijiazhuang 050061)

机构地区：[1]河北地质大学数理学院,石家庄050031 [2]河北经贸大学研究生学院,石家庄050061

出　　处：《华中师范大学学报（自然科学版）》2017年第4期426-428,共3页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金项目(11401158);河北省高等学校科学技术研究项目(QN2015240)

摘　　要：设k为非负整数,G是一个p点q边图,如果将G的边用k,k+1,k+2,…,k+q-1进行标号,而顶点标号模p运算后各不相同,则称G是k-边优美的.对于所有满足G为k-边优美图的非负整数k所构成的集合称为图G的边优美指标集.该文给出了图G=(V,E)为k-边优美的定义,根据轮图的特殊性质,讨论了S(3,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(3,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(3,n)的边优美指标集问题.Let kbe a nonnegative integer,and Gbe a graph with pvertices and qedges.The graph Gis 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 →Zpis a bijection too.We denote Gis 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 nis even.

关 键 词：边优美图 k-边优美 边优美指标集 S(3 n)图 

分 类 号：O157[理学—数学]