A New Distance-Regular Graph Associated to the Mathieu Group M 10
A.E. Brouwer
, J.H. Koolen2
and R.J. Riebeek3
2Graduate School of Mathematics, Kyushu University, 6-10-1 Hakozaki Higashi-ku Fukuoka 812 Japan
DOI: 10.1023/A:1008685726957
Abstract
We construct a bipartite distance-regular graph with intersection array {45, 44, 36, 5; 1, 9, 40, 45} and automorphism group 3 5 :(2 \times M 10) (acting edge-transitively) and discuss its relation to previously known combinatorial structures.
Pages: 153–156
Keywords: distance-regular graph; Mathieu group; spectra of graph
Full Text: PDF
References
1. E.R. Berlekamp, J.H. van Lint and J.J. Seidel, “A strongly regular graph derived from the perfect ternary Golay code,” A survey of combinatorial theory, Symp. Colorado State Univ., 1971 J.N. Srivastava et al., eds., North Holland, 1973.
2. A.E. Brouwer, A.M. Cohen and A. Neumaier, Distance-regular graphs, Springer, Heidelberg, 1989.
3. A.E. Brouwer and W.H. Haemers, “Structure and uniqueness of the (81,20,1,6) strongly regular graph,” Discrete Math. 106/107 1992, 77-82.
4. M. Sch\ddot onert et al., GAP: Groups, Algorithms and Programming, Aachen, April 1992.
5. B.D. McKay, “Nauty users guide (version 1.5)”, Technical Report TR-CS-90-02, Computer Science De- partment, Australian National University, 1990.
6. R.J. Riebeek, “Halved graphs of distance-regular graphs,” Master's thesis, Eindhoven Univ. of Techn., June 1992.
2. A.E. Brouwer, A.M. Cohen and A. Neumaier, Distance-regular graphs, Springer, Heidelberg, 1989.
3. A.E. Brouwer and W.H. Haemers, “Structure and uniqueness of the (81,20,1,6) strongly regular graph,” Discrete Math. 106/107 1992, 77-82.
4. M. Sch\ddot onert et al., GAP: Groups, Algorithms and Programming, Aachen, April 1992.
5. B.D. McKay, “Nauty users guide (version 1.5)”, Technical Report TR-CS-90-02, Computer Science De- partment, Australian National University, 1990.
6. R.J. Riebeek, “Halved graphs of distance-regular graphs,” Master's thesis, Eindhoven Univ. of Techn., June 1992.