Pappus graph

The automorphism group of the Pappus graph is a group of order 216. It acts transitively on the vertices, on the edges and on the arcs of the graph. Therefore the Pappus 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 Pappus graph, referenced as F018A, is the only cubic symmetric graph on 18 vertices. The characteristic polynomial of the Pappus graph is (x-3) x^4 (x+3) (x^2-3)^6. It is the only graph with this characteristic polynomial, making it a graph determined by its spectrum. ==Gallery==

Image:Pappus graph colored.svg|Pappus graph coloured to highlight various cycles. Image:Pappus graph 3color edge.svg|The chromatic index of the Pappus graph is 3. Image:Pappus graph 2COL.svg|The chromatic number of the Pappus graph is 2. Image:Pappus graph as regular map.png|The Pappus graph embedded in the torus, as a regular map with nine hexagonal faces. Image:Pappus-graph-on-torus.png|The Pappus graph and associated map embedded in the torus. == References ==