Study On Friendly Index Sets Of P_n^[n/2] Graph

Graph theory is one ofthe important contents in discrete mathematics,the object of its study is graph.Graph theory,which is used to represent the actual problem in a graph or network consisting of a number of points and a line connecting two points.Nowadays,it has been widely used in logistics transportation,Internet address communication,astronomy,X-ray,circuit design,code technology,coding theory and data base management.One of the important contents in graph theory is the labeling problem,which has a very good research value.The labeling problem of graphs begins with a Conjecture proposed by G.Ringelin 1963,as well as the famous Graceful Tree Conjecture proposed by A.Rosain 1966.1n 1987,Cahit defined the cordial graph,and later he proved the cordiality of Kn,Km,n,friendship graph C3(t),fans and wheel Wn.Lee and Ng defined the friendly index set of graphs G,and discussed the friendly index set of graph Cn,PCn,PC(n,p).If there is an injection f fro V(G)to {0,1} such that,when each edge uv is defined the f+(uv)= |f(u)-f(v)|.For each i ? {0,1},we order Vf(i)= {v|v?V(G),f(v)=i},Ef(i)={e|e}?E(G),f+(e)=i}.If |vf(1)-vf(0)|?1,we refer to f as the friendly labeling of graph G.The friendly label set of the graph is defined FI(G)= {|ef(1)?ef(0)|},which f is a friendly label.Some research results have been obtained in the study of graph pnk.Kang,Liang,Gao and Yang have studied the gracefulness and harmony of Pn2.Seoud,Abdel,Maqsoud and Sheeham proved that Pn3 is harmonious,and supposed if k>3,Pnk is not harmonious.This paper studies the friendly index set of Pn[n/2].Discuss the friendly index set of thesefour cases:n?1(mod 4),n?2(mod 4),n?3(mod 4),n?0(mod 4),when using the method of combination of numbers.And give the correspondingproof,finally get the conclusion.