Distance-regular graphs

ER Van Dam, JH Koolen, H Tanaka - arXiv preprint arXiv:1410.6294, 2014 - arxiv.org
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 …

[HTML][HTML] Taut distance-regular graphs and the subconstituent algebra

MS MacLean, P Terwilliger - Discrete mathematics, 2006 - Elsevier
We consider a bipartite distance-regular graph Γ with diameter D⩾ 4 and valency k⩾ 3. Let X
denote the vertex set of Γ and fix x∈ X. Let Γ22 denote the graph with vertex set X˘={y∈ …

[HTML][HTML] Bipartite distance-regular graphs: The Q-polynomial property and pseudo primitive idempotents

MS Lang - Discrete Mathematics, 2014 - Elsevier
Let Γ denote a bipartite distance-regular graph with diameter at least 4 and valency at least
3. Fix a vertex of Γ and let T denote the corresponding Terwilliger algebra. Suppose that Γ is …

[HTML][HTML] Pseudo primitive idempotents and almost 2-homogeneous bipartite distance-regular graphs

MS Lang - European Journal of Combinatorics, 2008 - Elsevier
Let Γ denote a bipartite distance-regular graph with diameter D≥ 4, valency k≥ 3 and
intersection numbers ci, bi (0≤ i≤ D). By a pseudo cosine sequence of Γ we mean a …

Bipartite distance-regular graphs and taut pairs of pseudo primitive idempotents

MS MacLean, Š Miklavič - Algebraic Combinatorics, 2019 - numdam.org
Let Γ denote a bipartite distance-regular graph with diameter D⩾ 4, valency k⩾ 3, and
intersection numbers ci, bi (0⩽ i⩽ D). By a pseudo cosine sequence of Γ we mean a …