【摘要】 对于一个简单无向连通图G(V,E)，若存在映射f:E(G)→{1,2，?，|E|}，且对于图中所有相邻且度相同的顶点，都有标号和相同，则称f为图G的邻点可约边标号（AVREL）.本文在学习研究已有图标号算法的基础上，设计了一种启发式搜索算法，利用该算法对15个顶点以内的联图进行标号，得到了邻点可约边标号的结果集.接着分析结果集，总结圈图与路图、星图和完全图形成的各类联图在有限点内的标号规律，并给出相关定理及证明.更多还原

【Abstract】 For a simple undirected connected graph G(V,E), f is said to be the adjacent vertex reducible edge labeling(AVREL) of the graph G if there exists a mapping f:E(G) →{1,2,…,|E|} that is labeled and identical for all adjacent vertices in the graph with the same degree. On the basis of learning and studying the existing graph labeling algorithms, a heuristic search algorithm is designed, using which to label the union graphs with 15 vertices or less, and obtain the result set of adjacent vertex reducible edge labeling. The result set is analyzed to summarize the labeling laws within finite points for various types of union graphs formed by circle graphs and path graphs, star graphs and complete graphs, and the related theorems and proofs are given.更多还原