Non-Bipartite Distance-Regular Graphs with Diameters 5, 6 and a Smallest Eigenvalue

摘要

Let C be a non-bipartite distance-regular graphs with valancy k, diameter D and a smallest eigenvalue theta(min). In 2019, Qiao, Jing and Koolen classified the non-bipartite distance-regular graphs with theta(min) <= D-1/D k for D = 4; 5. In this paper, we classify the non-bipartite distance-regular graphs with theta(min) <= -D-2/D-1 k for D = 5, 6. We remark that the technique of this paper is an extension of the approach taken by Qiao, Jing and Koolen on the study of non-bipartite distance-regular graphs in 2019.