The Hoffman-Singleton Graph and its Automorphisms
Paul R. Hafner
DOI: 10.1023/A:1025136524481
Abstract
We describe the Hoffman-Singleton graph geometrically, showing that it is closely related to the incidence graph of the affine plane over 
5. This allows us to construct all automorphisms of the graph.
5. This allows us to construct all automorphisms of the graph.Pages: 7–12
Keywords: hoffman-singleton graph; automorphisms; biaffine plane
Full Text: PDF
References
1. C.T. Benson and N.E. Losey, “On a graph of Hoffman and Singleton,” J. Combin. Theory 11 (1971), 67-79.
2. A.E. Brouwer, A.M. Cohen, and A. Neumaier, Distance-Regular Graphs, Springer-Verlag, 1989.
3. A.R. Calderbank and D.B. Wales, “A global code invariant under the Higman-Sims group,” J. Algebra 75 (1982), 233-260.
4. C. Fan and A.J. Schwenk, “Structure of the Hoffman-Singleton graph,” Congr. Numer. 94 (1993), 3-8.
5. W.H. Haemers, “A new partial geometry constructed from the Hoffman-Singleton graph,” in Finite Geometries and Designs, P.J. Cameron, J.W.P. Hirschfeld, D.R. Hughes (Eds.), Cambridge University Press, Cambridge, 1981, 119-127.
6. P.R. Hafner, “Geometric realisation of the graphs of McKay-Miller- \check Sirá\check n,” submitted.
7. D.G. Higman, “Primitive rank 3 groups with a prime subdegree,” Math. Z. 91 (1966), 70-86.
8. A.J. Hoffman and R.R. Singleton, “On Moore graphs with diameters 2 and 3,” IBM J. Res. Dev. 4 (1960), 497-504.
9. L.O. James, “A combinatorial proof that the Moore (7,2) graph is unique,” Utilitas Mathematica 5 (1974), 79-84.
10. B.D. McKay, M. Miller, and J. \check Sirá\check n, “A note on large graphs of diameter two and given maximum degree,” J. Combin. Theory Ser. B 74 (1998), 110-118.
2. A.E. Brouwer, A.M. Cohen, and A. Neumaier, Distance-Regular Graphs, Springer-Verlag, 1989.
3. A.R. Calderbank and D.B. Wales, “A global code invariant under the Higman-Sims group,” J. Algebra 75 (1982), 233-260.
4. C. Fan and A.J. Schwenk, “Structure of the Hoffman-Singleton graph,” Congr. Numer. 94 (1993), 3-8.
5. W.H. Haemers, “A new partial geometry constructed from the Hoffman-Singleton graph,” in Finite Geometries and Designs, P.J. Cameron, J.W.P. Hirschfeld, D.R. Hughes (Eds.), Cambridge University Press, Cambridge, 1981, 119-127.
6. P.R. Hafner, “Geometric realisation of the graphs of McKay-Miller- \check Sirá\check n,” submitted.
7. D.G. Higman, “Primitive rank 3 groups with a prime subdegree,” Math. Z. 91 (1966), 70-86.
8. A.J. Hoffman and R.R. Singleton, “On Moore graphs with diameters 2 and 3,” IBM J. Res. Dev. 4 (1960), 497-504.
9. L.O. James, “A combinatorial proof that the Moore (7,2) graph is unique,” Utilitas Mathematica 5 (1974), 79-84.
10. B.D. McKay, M. Miller, and J. \check Sirá\check n, “A note on large graphs of diameter two and given maximum degree,” J. Combin. Theory Ser. B 74 (1998), 110-118.