… Many constructions and results for strongly regular graphs are the d = 2 special case of
corresponding results for distance-regular graphs. The monograph [54] is devoted to the …

This is a survey of distance-regular graphs. We present an introduction to distance-regular
graphs for the reader who is unfamiliar with the subject, and then give an overview of some …

… For a distance-regular graph with diameter 3, we will show that the … distance-regular graph
Γ with diameter 3 is called Shilla if θ 1 = a 3 . It follows that for a Shilla distance-regular graph …

… As a particular case, we obtain the following new characterization of distance-regular
graphs: A graph 1, with adjacency matrix A, is distance-regular if and only if 1 has spectrally …

… characterizations of distance-regular graphs, we study ‘almost distanceregular graphs’.
We … We also give several characterizations of punctually distance-regular graphs that are …

… In this article, the second largest and minimal eigenvalue of a distance-regular graph turn …
Let denote a distance-regular graph with diameter d ≥ 3, and eigenvalues θ0 > θ1 > ··· > θd…

… Given a nontrivial primitive idempotent E of a distance-regular graph/- with diameter d ~> 3,
we obtain an inequality involving the intersection numbers of F for each integer i (3 ~< i ~< d)…

… In the next two sections, we take a closer look at the Terwilliger algebra of a distance-regular
graph: In Section 3, we consider its primitive idempotents and its irreducible modules, and …

… When studying metric dimension, distance-regular graphs are a natural class of graphs to …
of distance-regular graphs. It is a straightforward exercise to verify that the complete graph Kn …

… In this paper we prove that distance regular graphs with diameter d have at … distance
regular graph which gives the distinct D-eigenvalues. We also prove that distance regular graphs …