Algebraic Properties
The automorphism group of the Heawood graph is isomorphic to the projective linear group PGL2(7), a group of order 336. It acts transitively on the vertices, on the edges and on the arcs of the graph. Therefore the Heawood graph is a symmetric graph. It has automorphisms that take any vertex to any other vertex and any edge to any other edge. According to the Foster census, the Heawood graph, referenced as F014A, is the only cubic symmetric graph on 14 vertices.
The characteristic polynomial of the Heawood graph is . It is the only graph with this characteristic polynomial, making it a graph determined by its spectrum.
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