关于皇冠Q_n调和性的研究

Study on harmoniousness of the crown Q_n

皇冠Q_n(n≥3)是一类调和图。研究表明,从皇冠Q_n(2|n)去掉n-1条悬挂边则不能保持其调和性;从皇冠Q_n(2|n)去掉一条悬挂边而能保持其调和性;从皇冠Q_n(2|n)连续去掉两条悬挂边而能保持其调和性。问题是:从皇冠最多去掉多少条悬挂边,还能保持其调和性?基于现有结论,给出:从皇冠Q_n(2|n,n≥6)连续去掉三条悬挂边而能保持其调和性;从皇冠Q_6连续去掉四条悬挂边则不能保持其调和性;从皇冠Q_n(2|n,n≥8)连续去掉四条悬挂边而能保持其调和性;并猜想:从皇冠Q_n(2|n)最多连续去掉n/2条悬挂边而能保持其调和性。

The crown Qn （ n≥ 3 ） is a kind of harmonious graphs. Previous studies showed that ： the har- moniousness can not be preserved if deleting n-1 pendent edges from crown Qn（21n） ; the harmonious- ness can he preserved if deleting one pendent edge from crown Qn （21 n） ; the harmoniousness can be pre- served if deleting two pendent edges continuously from crown Qn （21 n）. Like this, a question is raised nationally： How many pendent edges up to remove from the crown can preserve the harmoniousness？ It is showed that deleting three pendent edges continuously from Qn （2/n, n≥6） can preserve the harmonious- ness; deleting four pendent edges continuously from Q6 can not preserve the harmoniousness; deleting four pendent edges continuously from Qn （21n, n ≥ 8 ） can preserve the harmoniousness. And suspect that n the harmoniousness can be preserved by up to remove n/2 pendent edges continuously from crown Q6 （21 n）.