单圈图的解析(英文)

On dissection of unicyclic graphs

得到了一些特殊图类的解析值.利用数学归纳和分类讨论的方法,给出固定阶数的单圈图的解析的紧的界.证明了在所有阶数为n的单圈图中,图△_(n-3)取得最小的a(G)和b(G);图K_(1,n-1)^+取得最大的a(G)和b(G).这里图△_(n-3)是由联结K_3一个顶点和P_(n-3)的一个端点而得到,图K_(1,n-1)^+是由联结图K_(1,n-1)中两个度为1的顶点而得到.

By the principle of mathematical induction and classified discussion, the sharp bounds for dissection of unicyclic graphs of a fixed order were given. Among all unicyclic graphs of order n（n ≥ 6）, the graph △n-3 has the minimum a（G） and b（G）, and the graph K1,n-1^＋ has maximum a（G） and b（G）, where △n-3 denotes the graph obtained from K3 and K1,n-1^＋ by joining a vertex of K3 to one endvertex of Pn-3, and K1,n-1^＋ denotes the graph K1,n-1^＋ obtained from K1,n-1 by joining its two vertices of degree one.