Geometric distance-regular graphs without 4-claws
Combinatorics
2011-01-04 v1 Spectral Theory
Abstract
A non-complete \drg is called geometric if there exists a set of Delsarte cliques such that each edge of lies in a unique clique in . In this paper, we determine the non-complete distance-regular graphs satisfying \max \{3, 8/3}(a_1+1)\}<k<4a_1+10-6c_2. To prove this result, we first show by considering non-existence of 4-claws that any non-complete distance-regular graph satisfying \max \{3, \8/3}(a_1+1)\}<k<4a_1+10-6c_2 is a geometric \drg with smallest eigenvalue -3. Moreover, we classify the geometric \drg s with smallest eigenvalue -3. As an application, 7 feasible intersection arrays in the list of \cite[Chapter 14]{bcn} are ruled out.
Cite
@article{arxiv.1101.0440,
title = {Geometric distance-regular graphs without 4-claws},
author = {Sejeong Bang},
journal= {arXiv preprint arXiv:1101.0440},
year = {2011}
}