双圈图边幻和全标号

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摘要图的边幻和全标号是指图G(p，q)中任意一条边与其关联顶点的标号之和等于常数，且点和边的所有标号值一一映射到集合.该文针对双圈图，设计了一种边幻和标号判定算法，利用该算法可以得到15个点内的所有双圈图边幻和全标号.通过结果分析，找到了两类双圈图的标号规律，定义了新的图运算符号CnΔCl SymbolQCpSm和CnΔCl ΔSm来刻画这两类图，总结了若干定理并给出证明，进一步猜测当顶点数p≥16时，相关结论仍然成立.

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	邵淑宏
	李敬文
	顾彦波
	王笔美

关键词 ：双圈图, 边幻和图, 边幻和标号, 算法

Abstract：The edge-magic total labelling of a graph G (p， q) means that the sum of labellings of any edge and its incident vertice is equal to a constant ， and the mapping of all labelling values of vertice and edges is the set . In this paper， a judge algorithm is designed to get all edge-magic total labelling of bicyclic graphs within 15 vertices. Through the analysis of the results， finding the rules of edge-magic total labelling for two kinds of bicyclic graphs， and defining the new graph operational symbols CnΔClSymbolQCpSm and CnΔClΔSm to describe such graphs， several theorems are summarized and proved finally. It is further conjectured that the relevant conclusions are still valid when the vertex p≥16.

Key words： bicyclic graphs edge-magic graphs edge-magic total labelling algorithms

收稿日期: 2020-12-01

引用本文:

邵淑宏,李敬文,顾彦波,王笔美. 双圈图边幻和全标号[J]. 华中师范大学学报(自然科学版), 2020, 54(6): 918-926.
SHAO Shuhong,LI Jingwen,GU Yanbo,WANG Bimei. Edge-magic total labelling of bicyclic graphs. journal1, 2020, 54(6): 918-926.

链接本文:

https://journal.ccnu.edu.cn/zk/CN/ 或 https://journal.ccnu.edu.cn/zk/CN/Y2020/V54/I6/918