Abstract：The adjacent vertex reducible total labeling (AVRTL) of a graph G(V，E) is a bijection from V(G)∪E(G) to the set of consecutive integers {1,2，…，|V(G)|＋|E(G)|}， and the sum of the labels is the same for all adjacent vertices in the graph with the same degree， as S(u)＝f(u)＋∑Gf(uw) . Combining with real-world problems， a new AVRTL algorithm is designed by drawing on the ideas of traditional intelligent algorithms such as the genetic algorithm and bee colony algorithm， which uses circular， iterative merit-seeking to obtain the adjacent vertex reducible total labeling results of all bicyclic graphs within a finite number of points by means of preprocessing functions and adjustment functions. By analyzing the experimental results， the labeling rules of several types of graphs were found， several theorems were summarized， and proofs were given. Finally， the conjecture was given that all bicyclic graphs are AVRTL graphs.
2024, Vol. 58 
