1968年，Vizing提出猜想:如果图$G$是$\Delta$-临界图, 则其独立数$\alpha (G)$满足$\alpha (G)\leqslant\dfrac{n}{2}$。这一猜想至今仍未解决。本文对于不含$度点的最大度较小的临界图, 证明当最大度$\Delta\in\{3, 4, 5, 6\}$时, 独立数$\alpha (G)\leqslant\dfrac{7\Delta-6}{12\Delta-6}|V|$;当$\Delta\in\{7, 8, 9\}$时, 独立数$\alpha (G)\leqslant\dfrac{4\Delta-3}{7\Delta-3}|V|$。

In 1968, Vizing conjectured for any edge chromatic critical graph $G$ with maximum degree $\Delta$ and independence number $\alpha(G)$, $\alpha(G)\leqslant\dfrac{n}{2}$. This conjecture is still open. In this paper, we proved that $\alpha(G)\leqslant\dfrac{7\Delta-6}{12\Delta-6}|V|$ for $\Delta\in\{3, 4, 5, 6\} $ and $\alpha(G)\leqslant \dfrac{4\Delta-3}{7\Delta-3}|V|$ for $\Delta\in\{7, 8, 9\}$.