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edit approved Jun 26, 2013 at 10:54
Andrew Uzzell
edit approved Jun 26, 2013 at 10:54
Andrew Uzzell
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I just found one of these graphs. It is constructed as follows:

In A_5$A_5$, let C$C$ be the class with 20$20$ elements and let C$C$ be the vertex set. An edge is a pair (x,y)$(x,y)$ where xy is in C$xy \in C$. Then there are 60$60$ edges. Call the graph G$G$. Then Aut(G)

Then $\operatorname{Aut}(G)$ is C_2 x S_5; G$C_2 x S_5$; $G$ has girth 3$3$, degree 6$6$, and Chromatic Number 4chromatic number $4$. It is vertex- and edge transitive-transitive.

I just found one of these graphs. It is constructed as follows:

In A_5 let C be the class with 20 elements and let C be the vertex set. An edge is a pair (x,y) where xy is in C. Then there are 60 edges. Call the graph G. Then Aut(G) is C_2 x S_5; G has girth 3, degree 6, and Chromatic Number 4. It is vertex and edge transitive.

I just found one of these graphs. It is constructed as follows:

In $A_5$, let $C$ be the class with $20$ elements and let $C$ be the vertex set. An edge is a pair $(x,y)$ where $xy \in C$. Then there are $60$ edges. Call the graph $G$.

Then $\operatorname{Aut}(G)$ is $C_2 x S_5$; $G$ has girth $3$, degree $6$, and chromatic number $4$. It is vertex- and edge-transitive.

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Steve Humphries
Steve Humphries
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I just found one of these graphs. It is constructed as follows:

In A_5 let C be the class with 20 elements and let C be the vertex set. An edge is a pair (x,y) where xy is in C. Then there are 60 edges. Call the graph G. Then Aut(G) is C_2 x S_5; G has girth 3, degree 6, and Chromatic Number 4. It is vertex and edge transitive.