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In this paper, through the joint-tree model we obtain that the genus of Wn+v equals 0 if the three neighbors of v are in the same face boundary of P(Wn); otherwise, {\\deg}(Wn + v) = 1, where P(Wn) is the unique planar embedding of Wn. In addition, via the independent set, we provide a lower bound on the maximum genus of graphs, which may be better than both the result of D. Li & Y. Liu and the result of Z. Ouyang etc: in Europ. J. Combinatorics. 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