Date: Sat, Dec 12, 2015
Time: 16:40 - 17:40
Venue: Middle Meeting Room
Title: On Q-polynomial distance-regular graphs of type 2
In 1986 Terwilliger  classified all Q-polynomial distance-regular graphs of type 2 with diameter at least 14. We improve this diameter bound. In fact, if the diameter of a Q-polynomial distance-regular graph $\Gamma$ of type 2 is less than 14, then some of arguments of the proof from  are not valid. Assuming that the diameter is at least 8 and studying possible locations of the roots of the Terwilliger polynomial of $\Gamma$ (recently calculated in ), we replace these arguments with their slightly extended version.
This is joint work with Jack Koolen.
Slides: View slides
 P. Terwilliger, A class of distance-regular graphs that are Q-polynomial, J. Combin. Theory Ser. B, 40(2):213-223, 1986.
 A.L. Gavrilyuk, J.H. Koolen, The Terwilliger polynomial of a Q-polynomial distance-regular graph and its application to pseudo-partition graphs, Linear Algebra Appl., 466:117-140, 2015.