The Turán number for a graph H, denoted by \(\text {ex}(n,H)\), is the maximum number of edges in any simple graph with n vertices which doesn’t contain H as a subgraph. In this paper we find the lower and upper bounds for \(\text { ex}(n,W_{2t+1})\). We show that if \(n\ge 4t\), then \(\text { ex}(n,W_{2t+1})\ge \left\lfloor \lfloor \frac{2n+t}{4}\rfloor (n+\frac{t-1}{2}-\lfloor \frac{2n+t}{4}\rfloor )\right\rfloor +1.\) We also show that for sufficiently large n and \(t\ge 5\), \(\text { ex}(n,W_{2t+1})\le \frac{ n^2 }{4}+{t-1\over 2}n\). Moreover we find the exact value of the Turán number for \(W_9\). That is, we show that for sufficiently large n, \(\text { ex}(n,W_9)= \lfloor \frac{n^2}{4}\rfloor +\lceil \frac{3}{4}n\rceil +1\).

用\（\ text {ex}（n，H）\）表示的图H的Turán数是具有n个顶点且不包含H作为子图的任何简单图的最大边数。在本文中，我们找到\（\ text {ex}（n，W_ {2t + 1}）\）的上下限。我们证明如果\（n \ ge 4t \），则\（\ text {ex}（n，W_ {2t + 1}）\ ge \ left \ lfloor \ lfloor \ frac {2n + t} {4} \ rfloor（n + \ frac {t-1} {2}-\ lfloor \ frac {2n + t} {4} \ rfloor）\ right \ rfloor +1。\）我们也证明了对于足够大的n和\（t \ ge 5 \），\（\ text {ex}（n，W_ {2t + 1}）\ le \ frac {n ^ 2} {4} + {t-1 \ over 2} n \）。此外，我们找到\（W_9 \）的图兰数的确切值。也就是说，我们表明对于足够大的n，\（\ text {ex}（n，W_9）= \ lfloor \ frac {n ^ 2} {4} \ rfloor + \ lceil \ frac {3} {4} n \ rceil +1 \）。