联图K1,1,3∨Cn的交叉数

摘要

A join graph denoteted by G∨H , is illustrated by connecting each vertex of graph G to each vertex of graphH . Based on the result that the crossing numbers of K1,1,2 ∨Cn is Z(4,n)+()+3 obtained by Klesc, obtain that the crossing numbers of join products K1,1,3∨Cn as well as {K1,1,3 + e}∨Cn are Z(5,n)+n+()]+4?The proofs depend on theproperties about the join products, and using reduction to absurdity and elimination method. Moreover, a conjecture is givenon the crossing number of K1,1,m ∨Cn(m≥4) within the conjecture of ＇arankiewicz:cr?(K1,1,m ∨Cn) ≥ Z(m+2,n)+()+m+1,m≥4?%联图GVH 表示将G 的每个顶点与H 的每个顶点连边得到的图?在Klesc 给出的联图K1,1,2∨Cn 的交叉数为Z(4,n)+()+3)的基础上,根据联图的相关性质,运用反证法和排除法,得到了联图K1,1,3∨Cn 与{K1,1,3 + e}∨Cn 的交叉数均为Z(5,n)+n+()+4?并假设在Zarankiewicz 猜想成立的前提下,提出对K1,1,m ∨ Cn(m ≥ 4) 的交叉数的一个猜想:cr?(K1,1,m ∨Cn)≥Z(m+2,n)+()+m+1,m≥4?