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.