Hamilton线图中的泛圈性(英文)

Pancyclicity in Hamiltonian Line Graphs

对于图G的边e=uv定义d(e)=d(u)+d(v)这里d(u)和d(v)分别表示u和v的度．该文的主要结果是:对阶为n(n≥40)的简单连通图G,如果对G中任意两条边距离为2的边e1,e2都有d(e_1)+d(e_2)≥n,并且线图L(G)是Hamilton的,则L(G)是泛圈的,并且条件L(G)是Hamilton是必要的．如果对G中任意两条距离为l的边e_1,e_2都有d(e_2)+d(e_2)≥n,并且L(G)是Hamilton的,则上(G)也是泛圈的．’

Abstract:For any edgee = uv of a graph G.let d(e) = d(u) + d(v) where d(u) and d(v) are the degrees of the vertices u and v respectively.In this paper,the main results are as follows:Let G be a simple connected graph of order n(n≥40) . If L(G) is Hamiltonian and d(e1) + d(ti)n for any pair of edges e1, and e2, of G with d(e1 ,e2) = 2,then L(G) is pancyclic.and the condition 'L(G) is Hamiltonian' is necessary.Let G be a simple connected graph of order n(n≥40). If L(C) is Hamiltonian and d(e1) +d(e2t)n for any pair of edges e1t and e2 of G with d(e1,e2) = 1 .then L(G) is pancyclic.