S(7,n)的k-边优美的图标号  

On the k-edge-graceful indices of S(7,n)

作　　者：刘晓姗 王琦[2] LIU Xiaoshan;WANG Qi(School of Mathematical and Physical Sciences,Hebei GEO University,Shijiazhuang 050031,China;School of Mathematics and Statistics,Hebei University of Economics and Business,Shijiazhuang 050061,China)

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

出　　处：《华中师范大学学报（自然科学版）》2018年第6期765-767,共3页Journal of Central China Normal University：Natural Sciences

基　　金：国家社会科学基金项目(18BGL272)

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,ua∑(u,v)∈Ef(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.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,u→(u,v)∈E∑f(u,v)mod p 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.

关 键 词：边优美图 k-边优美 边优美指标集 S(7 n)图 

分 类 号：O157[理学—数学]