1) k-graceful
K-优美
1.
In this paper,we defined "m-foot"chain graphs, and discussed their gracefulness,obtaining the results that six kinds of "m-foot"chain graphs are k-graceful bigraphs,and we also gave their graceful labelings.
定义了"m-脚"链图(即在P2×Pn的m个顶点各粘接一条悬挂边),讨论了它的优美性,得到了6种情形下的"m-脚"链图是k-优美的二分图,并给出了相应的优美标号。
2) K-gracefulness
K-优美
1.
If max{m_1,m_2,…,m_n}≥n-2,we prove that umbrella graph is K-gracefulness, and also give some conclusions about K-gracefulness of unicyclic graphs.
条边,只要满足条件max{m_1,m_2,…,m_n}≥n-2,则所得图为K-优美,并且给出了一些单圈图的K-优美结论,其中K为任意非负整数。
2.
In this paper, we verify the k-gracefulness on the subdivision graph of the product graphs Pn and C2m, P2n and C2m+1,P.
该文定义:一个简单图G=（V,E）是k-优美的（k≥1为整数）,如果存在单射f:V（G）→{0,1,2,…,|E|+k-1}使得对所有的边uv∈E（G）,由f＊（VV）一丫（V）-/（V门导出的映射 f＊:E（G）→{k,k+1,…,|E|+k-1}是双射。
3) k-edge-graceful
k-边优美
1.
The condition is given out in which G=(V,E) is said to be k-edge-graceful graph.
给出了图G=(V,E)为k-边优美的充分条件,根据正则图的特殊性质,讨论了P2×Cn为k-边优美图的必要条件。
4) k-graceful graph
k优美图
1.
In [3],Lu xian proved that graph St(m)∪Kp,q is a k-graceful graph when k>1 and min{p,q}≥2.
路线等在[3]中证明了当k>1,且min{p,q}≥2时,图St(m)∪Kp,q是k优美图。
5) k graceful graph
k-优美图
6) K-graceful labelling
K-优美标号
补充资料：优美
①美好；美妙：姿态优美｜风景优美。②亦称“秀美”。美学范畴之一。与“崇高”相对。指事物呈现出婉约柔和、纤巧雅致的特性，以此唤起人们亲切、愉悦、平和、自由的审美感受。
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