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三类图的优美性和序列性

发表时间:2008-03-15  浏览量:1914  下载量:624
全部作者: 刘多宁,刘春峰
作者单位: 渤海大学数学系;渤海大学数学系;锦州市教育局
摘 要: 称图G是k—优美图,如果对任何正整数k存在一个单射,f : V(G){0,1,2,…,|E|+ k |- 1}使得由fˊ(uv)=|f(u)- f(v)| 导出的函数对所有的边e=uvE(G),其映射E(G){ k , k+1,…, |E|+ k -1}是一个双射。称图G是序列图,如果存在一个单射,: V(G){0,1,2,…,|E|-1}(如果G是树,则也包含|E|)使得由ˊ(uv)=(u)+(v) 所导出的函数对所有的边e=uvE(G),其映射E(G){c,c+1,…,c+|E|-1}是一个双射(其中c为某一非负整数)。本文给出了图Gi(m,n) (i=1,2,3)的k—优美标号和序列标号,用构造的方法证明了图Gi(m,n) (i=1,2,3)是k—优美图和序列图,因此也是调和图,并推广了原有的一些结果。
关 键 词: 图论;优美图;顶点标号;序列图
Title: The grapcefulness and sequential of three lass graph
Author: LIU Duoning,LIU Chunfeng
Organization: Department of Mathematics Bohai university;Department of Mathematice Science, Liaoning Instiute of Technology;Jinzhou Education Bureau
Abstract: A graph G is k—graceful if there is labeling f from the vertices of G to{0,1,2,…,|E|+ k - 1} such that the set of edge labels induced by the absalute value of the difference of the labels of adjacent vertices is{ k , k+1,…, |E|+ k -1}. A graph G is sequential if there is labeling f from the vertices of G to{0,1,2,…,|E| - 1} such that the set of edge labels induced by the absalute value of the difference of the labels of adjacent vertices is{c,c+1,…,c+|E|-1} .In the paper, we obtain the sequential labeling and k—graceful labeling for the graphs Gi(m,n) (i=1,2,3). therefore the harmoniousness of them are showed.
Key words: graph theory; graceful graph; vertex labelling; sequential graph
发表期数: 2008年7月第5期
引用格式: 刘多宁,刘春峰. 三类图的优美性和序列性[J]. 中国科技论文在线精品论文,2008,1(5):545-550.
 
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