On the characterization of the folded halved cubes by their intersection arrays (Q1404329)

A folded halved \(2m\)-cube is a distance-regular graph with intersection array \(\{b_0, b_1,\dots, b_{d-1}\); \(c_1, c_2,\dots, c_d\}\) such that \(d:= \lfloor{m\over 2}\rfloor\) and \[ \begin{gathered} b_i= (m- i)(2m- 2i- 1),\quad c_i= i(2i- 1)\qquad (0\leq i\leq d-1),\\ c_d= \begin{cases} d(2d- 1),\quad &\text{if }m\text{ is odd};\\ 2d(2d- 1),\quad &\text{if }m\text{ is even}.\end{cases}\end{gathered} \] The paper shows that the folded halved cubes of diameter \(d\geq 5\) and the larger folded halved cube of diameter 4 are uniquely determined by their intersection arrays. The result also suggests a characterization of all pseudo-partition graphs of diameter \(d\geq 5\).