A graph is a set of points called vertices connected by lines called edges. Here is a graph called the Petersen graph.

         0         
        /|\        
       / | \       
      /  |  \      
     /   |   \     
    /    |    \    
   /     5     \   
  /     / \     \  
 /     /   \     \ 
1---6-+-----+-9---4
|    \|     |/    |
|     X     X     |
|     |\   /|     |
|     | \ / |     |
|     |  X  |     |
|     | / \ |     |
|     |/   \|     |
|     7     8     |
|    /       \    |
|   /         \   |
|  /           \  |
| /             \ |
|/               \|
2-----------------3

An automorphism of a graph G is a function f:G→G such that f(xy)=f(x)f(y) for all x, y∈G. A vertex-transitive graph is a graph G such that there is an automorphism between any two vertices of G. An edge-transitive graph is a graph G such that there is an automorphism between any two edges of G.

1. Prove that the Petersen graph is vertex-transitive.
2. Prove that the Petersen graph is edge-transitive.

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Posted by MeaganLindsey on 2021-12-25 03:07:27