Adjacent vertex reducible edge labeling of the several compound graphs
LI Jingwen1, SUN Liangjing1,2, HUANG Cong1, WANG Jiang1
1.School of Electronic and Information Engineering， Lanzhou Jiaotong University， Lanzhou 730070， China；2.Gansu Provincial Big Data Center，Lanzhou 730070，China
Abstract：For a simple undirected connected graph GV,E， f is said to be the adjacent vertex reducible edge labeling （AVREL） of the graph G if there exists a mapping f:EG→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.
2025, Vol. 59 
