The Biggs–Smith graph
The automorphism group of the Biggs–Smith graph is a group of order 2448 isomorphic to the projective special linear group PSL(2,17). It acts transitively on the vertices, on the edges and on the arcs of the graph. Therefore the Biggs–Smith 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 Biggs–Smith graph, referenced as F102A, is the only cubic symmetric graph on 102 vertices.
The characteristic polynomial of the Biggs–Smith graph is : .
The chromatic number of the Biggs–Smith graph is 3.
The chromatic index of the Biggs–Smith graph is 3.
- Weisstein, Eric W., "Biggs–Smith Graph", MathWorld.
- Brouwer, A. E.; Cohen, A. M.; and Neumaier, A. Distance-Regular Graphs. New York: Springer-Verlag, 1989.
- Royle, G. F102A data
- Conder, M. and Dobcsányi, P. "Trivalent Symmetric Graphs Up to 768 Vertices." J. Combin. Math. Combin. Comput. 40, 41–63, 2002.
- E. R. van Dam and W. H. Haemers, Spectral Characterizations of Some Distance-Regular Graphs. J. Algebraic Combin. 15, pages 189–202, 2003
- On trivalent graphs, NL Biggs, DH Smith - Bulletin of the London Mathematical Society, 3 (1971) 155-158.