一类串图的1-维魔幻标号

1-Dimension Magical Lablings of String Graphs

如果有整数对（s_i,t_i）（i∈[1,m]）和一一映f：V（G）∪E（G）→[1,p＋q],对每一条边uv∈E（G）,使得f（u）＋f（v）=s_i＋t_if（uv）,则称f是图G的（s_i,t_i）^m_i=1-魔幻标号。进一步,若存在最小的正整数k,使得G的任何一个（s_i,t_i）^m_i=1-魔幻标号满足m≥k,则称G为k-维（s,t）-魔幻图。为此,定义了图G的魔幻全空间与向量空间,并用向量代数方法研究串图G,得到图G有1-维（s,t）-魔幻全标号。给出了1-维（s,t）-魔幻全标号与奇优美标号、对偶标号之间的关系,及用具有1-维-魔幻全标号的二部分（p,q）-图G来构造大规模的1-维-魔幻全标号图的方法。

If there are integer paires such that a bijection of a connected graph from to satisfies for each edge,then is called a magically labeling. Furthermore,if there is minimum integer such that an abitrary-magically labeling satisfies,is called a one-dimension magically labeling. Hence,we defined the space of the magic total labellings and vector,and got 1- dimension magically labeling of the string graphs,and make use of methods of a vector algebra to research string graphs. The connections between one-dimension magically labeling and several known labelings（ such as odd-graceful,dual lablings） are given. We presented a method to construct some large-scale graphs with the magic total lablings.