Doro Graph

The Doro graph is a distance-transitive and distance-regular graph on 68 vertices and with valency 12. It is the unique automorphic graph having intersection array {12,10,3;1,3,8} (Gordon and Levingston 1981). Its automorphism group is PGammaL(2,16)=PSigmaL(2,16), where PSigmaL_2(q) denotes the semidirect product of PSL_2(q) by Aut(GF(q)) (Gordon and Levingston 1981).

It has spectrum (-5)^(16)0^(34)4^(17)12 (van Dam 1996) and is therefore an integral graph.

The Doro graph is implemented in the Wolfram Language as GraphData["DoroGraph"].

Note that Koolen et al. (2023) use the term "Doro graph" to refer to the Hall graph (which was first considered by Doro), which is a different distance-regular graph that has intersection array {10,6,4,1;1,2,5}.

See also

Automorphic Graph, Doro Graph

Explore with Wolfram|Alpha


Brouwer, A. E.; Cohen, A. M.; and Neumaier, A. "The Even Orthogonal Case; The Doro Graph." §12.1 in Distance Regular Graphs. New York: Springer-Verlag, pp. 211, 225, and 374-379, 1989.Buekenhout, F. and Rowlinson, P. "The Uniqueness of Certain Automorphic Groups." Geom. Dedicata 11, 443-446, "Doro Graph from PSigmaL(2,16).", S. "Two New Distance-Transitive Graphs." Unpublished.Gordon, L. M. and Levingston, R. "The Construction of Some Automorphic Graphs." Geom. Dedicata 10, 261-267, 1981.Koolen, J. H.; Yu, K.; Liang, X.; Choi, H.; and Markowsky, G. "Non-Geometric Distance-Regular Graphs of Diameter at Least 3 With Smallest Eigenvalue at Least -3." 15 Nov 2023. Dam, E. R. "Graphs with Few Eigenvalues: An Interplay Between Combinatorics and Algebra." Ph.D. dissertation. Tilburg, Netherlands: Tilburg University, pp. 51-52, October 4, 1996.

Cite this as:

Weisstein, Eric W. "Doro Graph." From MathWorld--A Wolfram Web Resource.

Subject classifications