关键词: 单圈图, 界, 解析, 单圈图, 界, 解析

Abstract: 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
$n(n\geqslant 6)$, 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.

Key words: bound, dissection, unicyclic graphs, bound, dissection