关于线图上的等距圈和次泛圈

ON ISOMETRIC CYCLE AND SUBPANCYCLIC IN LINE GRAPHS

给定一个图G ,且满足min{d(u) +d(v) :u ,v∈E(G) }≥ 8。有下结论 :若C是G中的圈且满足dc(u ,v) =d(u ,v) , {u ,v} V(C)。当任一这样的圈C的长度不超过△ (G) +1时 ,线圈L(G)是次泛圈的且所给的条件都是最好可能的。

Let G be a graph with min{d(u)+d(v):uvE(G)}≥8.It is proved that if the length of any cycle C in G with d C(u,v)=d(u,v) for any {u,v}V(C) is at most △(G)+1,then its line graph L(G) is subpancyclic and the result is best possible.