Let $G=K_{3,7}$ be a complete bipartite graph with partitions $X=\{x_1,x_2,x_3\}$ and $Y=\{y_1,y_2,y_3,y_4,y_5,y_6,y_7\}$. We know that the genus of graph $G$ is $2$. If we delete three edges $\{x_1y_1\}$, $\{x_2y_2\}$ and $\{x_3y_3\}$ of graph $G$ and add three edges $\{x_1x_2\}$, $\{x_2x_3\}$ and $\{x_1x_3\}$ to graph $G$, then the genus of the resulting graph is again $2$?
Genus of Complete Bipartite Graph
A.M
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