Abstract
It is known that bipartite distance-regular graphs with diameter $D\geq 3$, valency $k\geq 3$, intersection number $c_2\geq 2$ and eigenvalues $k = \theta_0 > \theta_1 > \cdots > \theta_D$ satisfy $\theta_1\leq k-2$ and thus $\theta_{D-1}\geq 2-k$. In this paper we classify non-complete distance-regular graphs with valency $k\geq 2$, intersection number $c_2\geq 2$ and an eigenvalue $\theta$ satisfying $-k< \theta \leq 2-k$. Moreover, we give a lower bound for valency $k$ which implies $\theta_D \geq 2-k$ for distance-regular graphs with girth $g\geq 5$ satisfying $g=5$ or $ g \equiv 3~(\operatorname{mod}~4)$.
Publisher
The Electronic Journal of Combinatorics
Subject
Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics
Cited by
2 articles.
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