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 The Complete Bipartite Graph
[SageMath](http://doc.sagemath.org/html/en/reference/graphs/sage/graphs/generic_graph.html) math says the genus is $1$.



```
sage: G = Graph([[0,1],[0,2],[1,2],[0,4],[0,5],[0,6],[0,7],[0,8],[0,9],[1,3],[1,5],[1,6],[1,7],[1,8],[1,9],[2,3],[2,4],[2,6],[2,7],[2,8],[2,9]])
sage: G.genus()
1
sage: G.get_embedding()

{0: [1, 2, 4, 5, 6, 7, 8, 9],
 1: [0, 9, 2, 3, 6, 5, 8, 7],
 2: [0, 7, 6, 3, 1, 9, 8, 4],
 3: [1, 2],
 4: [0, 2],
 5: [0, 1],
 6: [0, 1, 2],
 7: [0, 2, 1],
 8: [0, 1, 2],
 9: [0, 2, 1]} 

```

