Distance-Regular Graphs with Strongly Regular Subconstituents
Anna Kasikova
DOI: 10.1023/A:1008653827221
Abstract
In [3] Cameron et al. classified strongly regular graphs with strongly regular subconstituents. Here we prove a theorem which implies that distance-regular graphs with strongly regular subconstituents are precisely the Taylor graphs and graphs with a 1 = 0 and a i 
{0,1} for i = 2,..., d.
{0,1} for i = 2,..., d.Pages: 247–252
Keywords: distance-regular graph; strongly regular graph; association scheme
Full Text: PDF
References
1. A.E. Brouwer, A.M. Cohen, and A. Neumaier, Distance-Regular Graphs, Springer, Berlin-Heidelberg, 1989.
2. E. Bannai and T. Ito, Algebraic Combinatorics. Association Schemes, Benjamin/Cummings, Menlo Park, CA, 1984.
3. P.J. Cameron, J.M. Goethals, and J.J. Seidel, “Strongly regular graphs having strongly regular subconstituents,” J. Algebra 55 (1978), 257-280.
4. J.J. Seidel, “On two-graphs and Shult Characterization of symplectic and orthogonal geometries over GF(2),” T.H.-Report 73-WSK-02, Technological University Eindhoven, Eindhoven, 1973.
5. E.E. Shult, “The graph extension theorem,” Proc. Am. Math. Soc. 33 (1972), 278-284.
6. D.E. Taylor, “Regular 2-graphs,” Proc. London Math. Soc. 35 (3-d series) (1977), 257-274.
2. E. Bannai and T. Ito, Algebraic Combinatorics. Association Schemes, Benjamin/Cummings, Menlo Park, CA, 1984.
3. P.J. Cameron, J.M. Goethals, and J.J. Seidel, “Strongly regular graphs having strongly regular subconstituents,” J. Algebra 55 (1978), 257-280.
4. J.J. Seidel, “On two-graphs and Shult Characterization of symplectic and orthogonal geometries over GF(2),” T.H.-Report 73-WSK-02, Technological University Eindhoven, Eindhoven, 1973.
5. E.E. Shult, “The graph extension theorem,” Proc. Am. Math. Soc. 33 (1972), 278-284.
6. D.E. Taylor, “Regular 2-graphs,” Proc. London Math. Soc. 35 (3-d series) (1977), 257-274.