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John Machacek
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SageMath math says the genus of $G$ 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]} 

SageMath math says the genus of $G$ 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]} 

SageMath 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]} 
Source Link
John Machacek
  • 7.9k
  • 1
  • 23
  • 40

SageMath math says the genus of $G$ 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]}