图(K_2∨)·(K_2∨■)的优美性及协调性  

Gracefulness and Harmonious of Graph(K_2∨)·(K_2∨■)

作　　者：路线[1] 潘伟[2] 刘铁军[3] 

机构地区：[1]吉林工程技术师范学院基础科学系,长春130052 [2]吉林大学数学学院,长春130012 [3]吉林大学计算机科学与工程学院,长春130012

出　　处：《吉林大学学报（信息科学版）》2006年第4期447-450,共4页Journal of Jilin University（Information Science Edition）

摘　　要：图的标号问题是组合数学的一个热门课题,在编码理论、网络、循环设计等许多领域都有重要应用。但对于一个图既是优美的又是协调的研究甚少。为此,对正整数k,n,m∈N+(N+为正整数集合),给出了一类图(K2∨Kn).(K2∨Km),并通过构造标号函数的方法,论证了当n=2k时,该图是优美图;同时也论证了当m=n-1(n≥2)时,该图是协调图。Labeling function of graph in combination mathematics has been a very topic, witch is put in use in so many fields such as coding theory, internet, and circulating design. The study that how to make graph not only graceful but also harmonious is not so popular, so it＇s very meanful to study the gracefulness and harmony of graph. The present paper gives a kind of graph （K2∨Kn）·（K2∨Km）, for natural numbers k, n, rn e N^＋ （N^＋ represents the set of positive integers）. By establishing the labeling function it is proved that the graph is a graceful graph, when n =2k and the graph is harmonious graph, when rn =n - 1 （n≥2）.

关 键 词：优美图 协调图 标号函数 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术] O157.9[自动化与计算机技术—计算机科学与技术]