Two distance-regular graphs
Andries E. Brouwer, Dmitrii V. Pasechnik
TL;DR
This paper constructs two new families of distance-regular graphs derived from dual polar graphs, revealing their structural relationships and properties.
Contribution
It introduces two specific families of distance-regular graphs based on dual polar graphs and explores their connection as extended bipartite doubles.
Findings
Construction of the subgraph of the dual polar graph of type B_3(q)
Construction of the subgraph of the dual polar graph of type D_4(q)
The D_4(q) graph is the extended bipartite double of the B_3(q) graph
Abstract
We construct two families of distance-regular graphs, namely the subgraph of the dual polar graph of type B_3(q) induced on the vertices far from a fixed point, and the subgraph of the dual polar graph of type D_4(q) induced on the vertices far from a fixed edge. The latter is the extended bipartite double of the former.
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