不含偶圈(n,m)-图匹配多项式的最大根

On the largest root of the matching polynomials of(n,m)-graphs without even cycles

令图G是具有n个顶点的简单连通图。图G的匹配多项式定义为∑_(k=0)^([n/2])(-1)^(k)m(G,k)x^(n-2k),其中m(G,k)是图G中k-匹配的数目,0≤k≤[n/2]。令Φ_(n,m)是具有n个顶点和m条边的不含偶圈图的集合,其中n≤m≤3(n-1)/2。本文介绍了四个新的比较匹配多项式最大根的变换方法,从而刻画了Φ_(n,m)中具有匹配多项式最大根的图。

Let G be a simple connected graph with n vertices.The matching polynomial of C is given by∑_(k=0)^([n/2])(-1)^(k)m(G,k)x^(n-2k),where m(C,)s the number of k-matchings in G with 0<k≤[n/2].Let Φ_(n,m). be the set of graphs with n vertices and m edges having no even cycles,where n≤m≤3(n-1)/2.In this paper,four new 2 transformations for comparing the largest roots of matching polynomials are introduced and the graph with the largest root of matching polynomial is characterized among graphs inΦ_(n,m).