The McGee graph
|Named after||W. F. McGee|
The McGee graph requires at least eight crossings in any drawing of it in the plane. It is one of five non-isomorphic graphs tied for being the smallest cubic graph that requires eight crossings. Another of these five graphs is the generalized Petersen graph G(12,5), also known as the Nauru graph.
The characteristic polynomial of the McGee graph is : .
The automorphism group of the McGee graph is of order 32 and doesn't act transitively upon its vertices: there are two vertex orbits, of lengths 8 and 16. The McGee graph is the smallest cubic cage that is not a vertex-transitive graph.
The crossing number of the McGee graph is 8.
The chromatic number of the McGee graph is 3.
The chromatic index of the McGee graph is 3.
The acyclic chromatic number of the McGee graph is 3.
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