Errera graph
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In the mathematical field of graph theory, the Errera graph is a graph with 17 vertices and 45 edges. Alfred Errera published it in 19211 as a counterexample to Kempe's erroneous proof of the four color theorem; it was named after Errera by .
In the mathematical field of graph theory, the Errera graph is a graph with 17 vertices and 45 edges. Alfred Errera published it in 1921 as a counterexample to Kempe's erroneous proof of the four color theorem; it was named after Errera by .
Properties
The Errera graph is planar and has chromatic number 4, chromatic index 6, radius 3, diameter 4 and girth 3. All its vertices are of degree 5 or 6 and it is a 5-vertex-connected graph and a 5-edge-connected graph. The Errera graph is not a vertex-transitive graph and its full automorphism group is isomorphic to the dihedral group of order 20, the group of symmetries of a decagon, including both rotations and reflections. The characteristic polynomial of the Errera graph is -(x^2-2 x-5) (x^2+x-1)^2 (x^3-4 x^2-9 x+10) (x^4+2 x^3-7 x^2-18 x-9)^2 .
External links
Text derived from https://en.wikipedia.org/w/index.php?oldid=1368680110 under CC BY-SA 4.0; modifications have been made.