一类二部图的奇优美性

The odd gracefulness of G

设L为简单无向图G的一个顶点标号,L称为图G的奇优美标号,若L满足:1)L为G的顶点集V到{0,1,…,2 E-1}的一个单射;2)由L′(e)=L(u)-L(v)(其中e=uv)决定的边标号L′是从G的边集E到{1,3,…,2 E-1}的一个双射。根据奇优美图的定义,研究了一类二部图G*的奇优美标号。

In light of the definition of odd graceful graph, this paper discusses the odd gracefulness of some bipartite graphs G＊. Let L be a vertex labeling of simple graph G, L is said to be a graceful labeling of G if L satisfies both the following-1）L is an injective mapping from V to {1,2,…,2 ｜E｜-1 };2）The function obtained by setting L＇ （e） =｜L（u）--L（v）｜ ,in which e=uv,is a bijective function from E （G） to {1,3,…, 2｜E｜-1}. According to the definition of odd graceful graph, this paper discusses the odd gracefulness of some bipartite graphs G＊.