图T_(1,1,m),Q(3,n)中有路因子的充分必要条件及T_(1,1,m),的匹配等价类

The Sufficient and Necessary Condition of Graph T_(1,1,m)and Q(3,n) Possessing Path Divisor and the Equivalent Graphs of T_(1,1,m)

如果一个图的匹配多项式可以被一个路的匹配多项式整除,我们就说这路是该图的一个路因子,路因子在刻画图的匹配等价类,研究匹配唯一性方面有很重要的作用·得到了T1,1,m,Q(3,n)中有路因子的充分必要条件.并且给出了T1,1,m,当m≠4k(k为正整数)时的匹配等价图类·

If a matching polynomial of a graph is exactly divided by a polynomial of a path we say the path is a path divisor of the graph. The path divisor plays an important role in characterizing the matching equivalent graphs of a graph and studying the uniqueness of matching. In this paper, we present a sufficient and necessary condition of graph T1,1,m and Q（3 ,n） possessing path divisor and prove the matching equivalent graphs of T1,1,m when n≠4k .