为了推广无爪图G在闭包运算下是唯一确定的并且保持路长不变这一结论,对包含无爪图的(K1,4;2)-图进行研究,主要采用逐一讨论、排除的方法对此类图的路长在闭包运算下保持不变的性质进行证明.结果表明:在已知K1∨P4-free或T3-free的(K1,4;2)-图在闭包运算下也唯一确定并且仍为(K1,4;2)-图的条件下,如果G是K1∨P4-free或T3-free的(K1,4;2)-图,则在闭包的运算下保持路长不变;K1∨P4-free或T3-free的(K1,4;2)-图G可迹当且仅当其闭包是可迹的,其中K1∨P4为一个点与长为4的路的联图,T3为K1,3与K2的并图.%To promote the conclusion of the closure of a claw-free graph G being well-definded and the length of a longest path in G or in its closure being the same,the (K1,4;2)-graphs containing claw-free graphs were studied.The property of the length of a longest path in this class of graph or in its closure being the same was proved by using the method of discuss-ing each kind of case one by one and rule out one by one.The results show that under the condition of any (K1,4;2)-graph being K1∨P4-free or T3-free whose closure is well-definded and is still a (K1,4;2)-graph,if G is a (K1,4;2)-graph which is K1∨P4-free or T3-free,the length of a longest path in G or in its closure is the same.A (K1,4;2)-graph which is K1∨P4-free or T3-free is traceable if and only if its closure is traceable,where K1∨P4 expresses the join graph of a vertex and a path whose length is four,and T3 expresses the union graph of K1,3 and K2.
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