1) odd graceful graph
奇优美图
1.
If there exists a mapping f: V→{0,1,2,…,2E|-1} which satisfies: u,v∈V,if u≠v,then f(u)≠f(v);max{ f(v)|v∈V}=2|E|-1; e 1,e 2∈E,if e 1≠e 2,then g(e 1)≠g(e 2),here g(e)=|f(u)-f(v)|,e=uv;{g(e)|e∈E}={1,3,5,…,2|E|-1 },then G is called an odd graceful graph,and f is called odd graceful labeling of G.
对于简单图G=,如果存在一个映射f:V→{0,1,2,…,2E|-1}满足:对任意的u,v∈V,若u≠v,则f(u)≠f(v);max{f(v)|v∈V}=2|E|-1;对任意的e1,e2∈E,若e1≠e2,则g(e1)≠g(e2),此处g(e)=|f(u)-f(v)|,e=uv;{g(e)|e∈E}={1,3,5,…,2|E|-1},则称G为奇优美图,f称为G的奇优美标号。
2) On the Odd-Graceful of Graph
关于图的奇优美性
3) odd graceful
奇优美
1.
In this paper, we define a class of new graph-spoon star graph and as wellas weak odd strong harmony graph, is defined, the writers give Stn P1C4’s odd graceful labeling、k- graceful labeling and weak odd strong harmony labeling,and prove that the Stn P1C4 is a odd graceful graph, k-graceful graph and weak odd strong harmony graph.
该文定义了一类新的图形——星勺图StnP1C4,并定义了图的次奇强协调性,同时给出了它的奇优美标号、k-优美标号及次奇强协调标号,从而证明了星勺图StnP1C4是奇优美图、k-优美图和次奇强协调图。
2.
In this paper,we obtain three kinds of graphs by adding some vertices and some edges on,and proved that the three kinds of graphs not only are allgraceful,odd graceful,but also are balanced graphs and alternating graphs.
本文通过在上增加一些顶点和边,得到了三种图,并得出此三种图均是优美的,奇优美的,也是交错图,平衡图,同时给出了相应的标号。
3.
It is shown that∪ni=1 Pli, ∪ni=1 Sli, ∪ni=1 Sli ∪∪ti=1 Pmi ,Cm ∪Pn and Cm ∪Cn are odd graceful, and that ∪ni=1 Cmi is odd graceful when mi ≡0(mod4).
讨论了并图∪ni=1Pli,∪ni=1Sli,∪in=1Sli∪∪it=1PmiCm∪Pn, Cm∪Cn和∪in=1Cmi,∪in=1Pli,∪in=1Sli,∪in=1Sli∪∪it=1PmiCm∪Pn, Cm∪Cn被证明了是奇优美的,∪in=1Cmi当mi≡0(mod4)时是奇优美的。
4) odd graceful labeling
奇优美标号
1.
If there exists a mapping f: V→{0,1,2,…,2E|-1} which satisfies: u,v∈V,if u≠v,then f(u)≠f(v);max{ f(v)|v∈V}=2|E|-1; e 1,e 2∈E,if e 1≠e 2,then g(e 1)≠g(e 2),here g(e)=|f(u)-f(v)|,e=uv;{g(e)|e∈E}={1,3,5,…,2|E|-1 },then G is called an odd graceful graph,and f is called odd graceful labeling of G.
对于简单图G=,如果存在一个映射f:V→{0,1,2,…,2E|-1}满足:对任意的u,v∈V,若u≠v,则f(u)≠f(v);max{f(v)|v∈V}=2|E|-1;对任意的e1,e2∈E,若e1≠e2,则g(e1)≠g(e2),此处g(e)=|f(u)-f(v)|,e=uv;{g(e)|e∈E}={1,3,5,…,2|E|-1},则称G为奇优美图,f称为G的奇优美标号。
5) graceful graph
优美图
1.
Simple graphs are all the subgraphs of graceful graphs;
简单图都是优美图的子图
2.
Cycles with two pendent edges are graceful graphs;
带两条悬挂边的回路是优美图
补充资料：图的减缩图(或称图子式)
图的减缩图(或称图子式)
minor of a graph
图的减缩图(或称图子式)【.皿以ofa脚户;MHHoPrpa中a」【补注】设G是一个图(graph)(可以有环及多重边).G的一个减缩图(nullor)是从G中接连进行下述运算而得的任何一个图: i)删去一条边; 五)收缩一条边; 说)去掉一个孤立顶点. NRobe由on与P.D.Se脚aour的图减缩定理(脚Ph nl的。r theon习11)如下所述:已知有限图的无穷序列G，，GZ，…，则存在指标i
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条