On geometric distance-regular graphs with diameter three

Title
On geometric distance-regular graphs with diameter three
Author(s)
방세정J.H. Koolen[ J.H. Koolen]
Issue Date
201402
Publisher
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
Citation
EUROPEAN JOURNAL OF COMBINATORICS, v.36, pp.331 - 341
Abstract
In this paper we study distance-regular graphs with intersection array {(t + 1)s. ts. (t - 1)(s + 1 - psi); 1, 2, (t + 1)psi} (1) where s. t. psi are integers satisfying t >= 2 and 1 <= psi <= s. Geometric distance-regular graphs with diameter three and c(2) = 2 have such an intersection array. We first show that if a distance-regular graph with intersection array (1) exists, then s is bounded above by a function in t. Using this we show that for a fixed integer t >= 2, there are only finitely many distance-regular graphs of order (s, t) with mallest eigenvalue -t -1, diameter D = 3 and intersection number c(2) = 2 except for Hamming graphs with diameter three. Moreover, we will show that if a distance-regular graph with intersection array (1) for t = 2 exists then (s, psi) = (15, 9). As Gavrilyuk and Makhnev (2013)[9] proved that the case (s, psi) = (15, 9) does not exist, this enables us to finish the classification of geometric distance-regular graphs with smallest eigenvalue -3, diameter D >= 3 and c(2) >= 2 which was started by the first author (Bang, 2013)[1]. (C) 2013 Elsevier Ltd. All rights reserved.
URI
http://hdl.handle.net/YU.REPOSITORY/33172http://dx.doi.org/10.1016/j.ejc.2013.06.044
ISSN
0195-6698
Appears in Collections:
이과대학 > 수학과 > Articles
Files in This Item:
There are no files associated with this item.
Export
RIS (EndNote)
XLS (Excel)
XML


qrcode

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

BROWSE