摘要:
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~$\Delta_{n-3}$~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~$\Delta_{n-3}$~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.
Abstract:
By the principle of mathematical induction and classifieddiscussion, the sharp bounds for dissection of unicyclic graphs of afixed order were given. Among all unicyclic graphs of order$n(n\geqslant 6)$, the graph $\Delta_{n-3}$ has the minimum $a(G)$and $b(G)$, and the graph $K_{1,n-1}^{+}$ has maximum $a(G)$ and$b(G)$, where $\Delta_{n-3}$ denotes the graph obtained from $K_{3}$and $P_{n-3}$ by joining a vertex of $K_{3}$ to one endvertex of$P_{n-3}$, and $K_{1,n-1}^{+}$ denotes the graph obtained from$K_{1,n-1}$ by joining its two vertices of degree one.
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