东南大学学报（英文版）2004，Vol.20Issue(2)：251-255,5.
哈密尔顿性、邻域并和无爪图的平方图
Hamiltonicity, neighborhood union and square graphs of claw-free graphs
摘要
Abstract
Let G be a graph, the square graph G2 of G is a graph satisfying V(G2)=V(G) and E(G2)=E(G)∪{uv: dist[JX+6x]G(u, v)=2}. In this paper, we use the technique of vertex insertion on l-connected (l=k or k+1, k≥2) claw-free graphs to provide a unified proof for G to be Hamiltonian, 1-Hamiltonian or Hamiltonian-connected. The sufficient conditions are expressed by the inequality concerning ∑ k I=0N(Yi) and n(Y) in G for each independent set Y={y0, y1, …, yk} of the square graph of G, where b (0＜b＜k+1) is an integer, Yi={yi, yi-1, …, yi-(b-1)}Y for I∈{0, 1, …, k}, where subscriptions of yjs will be taken modulo k+1, and n(Y)={v∈ V(G): dist(v, Y)≤2}.关键词
哈密尔顿性/无爪图/邻域并/插点/平方图Key words
Hamiltonicity/claw-free graph/neighborhood union/vertex insertion/square graph分类
数理科学引用本文复制引用
徐新萍..哈密尔顿性、邻域并和无爪图的平方图[J].东南大学学报（英文版）,2004,20(2):251-255,5.基金项目
The National Natural Science Foundation of China (No.19971043). （No.19971043）
