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.
作者
刘晓珊
王琦
LIU Xiaoshan WANG Qi(Institute of Mathematical and Physical Sciences, Hebei GEO University, Shijiazhuang 050031 Graduate School, Hebei University of Economics & Business, Shijiazhuang 050061)
出处
《华中师范大学学报(自然科学版)》
CAS
北大核心
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)