关于哈密尔顿指数的综述

The Hamiltonian Index of a Graph——A Survey

图G的线图L(G)是指以G的边集E(G)为顶点集且L(G)的2个顶点邻接当且仅当它们在G中有公共顶点.n次迭代线图Ln(G)递归地定义为L0(G)=G,Ln(G)=L(Ln-1(G))(n∈N={0,1,2,…}),其中L1(G)=L(G)并且假设Ln-1(G)非空,使得Ln(G)是哈密尔顿的最小整数n称为哈密尔顿指数,用h(G)表示.该文综述了(类)哈密尔顿指数的一些结果.

Let G be a simple graph. The line graph L（ G）of a graph G is a graph which has E（ G）as its vertex set and two vertices are adjacent in L（ G）if and only if they share an end vertex in G. The n-th iterated line graph Ln（G）is defined recursively by L0（G）=G,Ln（G）=L（Ln-1（G））（n∈N={0,1,2,…}）,where L1（G）=L（G） and Ln-1（ G）is assumed to be nonempty. The hamiltonian index of a graph G,denoted by h（ G）,is the smallest in-teger n such that Ln（G）is hamiltonian. The results of hamiltonian（like）indices of graphs have been summariczed.