Study On The Full Edge Friendly Index Sets Of Simple Graphs

Graph theory is a very important branch of combinatorial and discrete mathematics,as well as an important content of computer science.The main content of this paper is to deduce the point labeling from the edge labeling of graphs.A conjecture put forward by G.Ringel in 1963,and after the famous beautiful tree conjecture proposed in 1966.People began to pay close attention to the labeling problem of graphs.The labeling graphs in graph theory have an important theoretical value and a wide application background.Such as: cryptography,physical chemistry,geography,astronomy,network design,computer science and other fields have widely applied graph theory and its algorithms.At present,many domestic and foreign research achievements on full friendly index sets and full edge friendly index sets have been made.In this paper,we study the full edge friendly index sets of fan graphs and gear graphs in simple graphs.Specifically divided into:1.When n is even,the full edge friendly index set of the fan graph2.When n is an odd,the full edge friendly index set of the fan graph3.When n is even,the full edge friendly index set of the gear graph4.When n is odd,the full edge friendly index set of the gear graph FEFI(G_n)={-(2n+1),-(2n-3),…，-3,1…，2n-5,2n-1}。By studying the characteristics and labeling rules of the full-edge friendly index set of existing graphics and combining the graphs to find out the general rules.Then we get the conclusion of the full edge friendly index sets of fan graphs and gear graph in simple graph.Then corresponding proofs and examples are given to illustrate the correctness of the conclusions.