摘要
若对图G中任意一对距离为2的点x,y,存在u∈N(x)∩N(y),使得[u]N[x]∪N[y],则称G为半无爪图.许多关于无爪图的结果已经被推广到更大的图类———半无爪图,本文证明了下面的结果:(1)若G是半无爪图,x是G的一适宜点,G′为由G在x局部完备所得,则G′仍是半无爪图,但G′不一定是无爪图.(2)若G是半无爪图,则其闭包cl(G)是唯一确定的.并由(1)有推论:若G是半无爪图,则其闭包cl(G)仍是半无爪图.
A graph G is quasi claw-free if it satisfies the property： d （x, y ） = 2→there exists u ∈ N （x）∩ N （y） such that N[ u ] lohtain in N[ x ] ∪ N[ y ]. Many known results on claw-free graphs have been extended to the larger class of quasi claw-free graphs. In this paper, we show the following results： （ 1 ） Let G be a quasi claw-free graph and x be an eligible vertex of G. Let G＇ be a local completion of G at x. Then the graph G＇ is a quasi claw-free graph but it is not sure that G＇ is a claw-free graph. （2）Let G be a quasi claw-free graph.Then cl（G）is well defined. From（ 1 ）, we have the following corollary ：Let G be a quasi calw-free graph. Then cl（G）is still a quasi claw-free graph.
出处
《山东科学》
CAS
2006年第1期20-22,共3页
Shandong Science
基金
山东省教委科技计划项目(J01P01)
关键词
半无爪图
局部连通
闭包
quasi claw-free graphs
locally connected
closure
