The Terwilliger Algebra of the Incidence Graphs of Johnson Geometry

  • Qian Kong
  • Benjian Lv
  • Kaishun Wang
Keywords: Terwilliger algebra, Johnson graph, incidence graph, Johnson geometry


In 2007, Levstein and Maldonado  computed the Terwilliger algebra of the Johnson graph $J(n,m)$ when $3m\leq n$. It is well known that the halved graphs of the incidence graph $J(n,m,m+1)$ of Johnson geometry are Johnson graphs. In this paper, we determine the Terwilliger algebra of $J(n,m,m+1)$ when $3m\leq n$, give two bases of this algebra, and calculate its dimension.
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