Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8903168 | Discrete Mathematics | 2018 | 8 Pages |
Abstract
A non-complete distance-regular graph is called geometric if there exists a set C of Delsarte cliques such that each edge lies in exactly one clique in C. Let Î be a geometric distance-regular graph with diameter Dâ¥3 and smallest eigenvalue θD. In this paper we show that if Î contains an induced subgraph K2,1,1, then Dâ¤âθD. Moreover, if âθDâ1â¤Dâ¤âθD then D=âθD and Î is a Johnson graph. We also show that for (s,b)ââ{(11,11),(21,21)}, there are no distance-regular graphs with intersection array {4s,3(sâ1),s+1âb;1,6,4b} where s,b are integers satisfying sâ¥3 and 2â¤bâ¤s. As an application of these results, we classify geometric distance-regular graphs with Dâ¥3, θDâ¥â4 and containing an induced subgraph K2,1,1.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Sejeong Bang,