【作者】 张静；

【导师】 高振滨；

【作者基本信息】 哈尔滨工程大学 ， 数学， 2020， 硕士

【摘要】 图论是离散数学的一个分支,图的标号理论是图论中一个较新的理论。本文研究的是由图的边友好标号延伸出的边平衡指标集问题。1995年,Kong和Lee在《On edge balanced graph》中提出了边友好标号问题并定义了边平衡性和强边平衡性,从此人们开始研究各种图形的边平衡指标集问题。目前国内外已取得了不少关于边平衡指标集的研究成果。本文主要研究含弦圈图和圈图与路串联形成的图的边平衡指标集。具体分为:对于(?)(m(C4,P2+{u1,u3}),P2)图,有(1)当m整除5时,图的边平衡指标集为{0,1,2,...,4m/5};(2)当m除5余数为j(j=1,2,3,4)时,图的边平衡指标集为{0,1,2,...,4(m-j)/5+(j-1)}。对于(?)(m(C4,P2+{u2,u4}),P2)图,边平衡指标集为{0,2,4,...,2m}。对于(?)(m C4,P2)图,有(1)当m除6余0、2、4时,图的边平衡指标集为{0,1,2,...,m};(2)当m除6余1、3、5时,图的边平衡指标集为{0,1,2,...,m+1}。通过研究已有圈图与路的边平衡指标集的标号方法,结合所研究的图的特点,进行归纳总结,找出其普遍的规律,通过逻辑证明,得到上述图的边平衡指标集,并且通过例子验证了结论的正确性。更多还原

【Abstract】 Graph theory is a branch of discrete mathematics,the labeling of graph is a relatively new theory in graph theory.In this paper,we study the problem of edge balance index sets extended by edge-friendly labels of graph.In 1995,the edge-friendly labeling problem is proposed and the edge balance and strong edge balance are defined by Kong and Lee in the article《On edge-balanced graph》,from then on,people began to study the problem of edge balance index sets of various graph.At present,many domestic and foreign research achievements on edge balance index sets have been made.In this paper,we study the edge balance index sets of a graph formed in series with a path which cycle graphs containing one chord and cycle.Specifically divided into:For graph(?)(m(C4,P2+{u1,u3}),P2),there are(1)when m is divided by 5,the edge balance index sets of the graph is {0,1,2,...,4m/5};(2)when m is divided by 5 and the remainder is j,the value of j is 1 or 2 or 3 or 4,the edge balance index sets of the graph is {0,1,2,...,4(m-j)/5+(j-1)}.For graph(?)(m(C4,P2+{u2,u4}),P2),the edge balance index sets is ｛0,2,4,...,2m}.For graph(?)(mC4,P2),there are(1)when m is divided by 6 and the remainder is 0 or 2 or 4,the edge balance index sets of the graph is ｛0,1,2,...,m};(2)when m is divided by 6 and the remainder is 1 or 3 or 5,the edge balance index sets of the graph is ｛0,1,2,...,m+1}.By studying the labeling method of the edge balance index sets of the cycle and the path,and combining with the characteristics of the graphs studied,and summarize to find out the general rules.Through logical proof,the edge balance index sets of the above graph is obtained,and the correctness of the conclusion is verified by examples.更多还原