1-Homogeneous Graphs with Cocktail Party μ-Graphs

@article{Jurisic20031HomogeneousGW,
  title={1-Homogeneous Graphs with Cocktail Party μ-Graphs},
  author={A. Jurisic and J. Koolen},
  journal={Journal of Algebraic Combinatorics},
  year={2003},
  volume={18},
  pages={79-98}
}
Let Γ be a graph with diameter d ≥ 2. Recall Γ is 1-homogeneous (in the sense of Nomura) whenever for every edge xy of Γ the distance partition{{z ∈ V(Γ) | ∂(z, y) = i, ∂(x, z) = j} | 0 ≤ i, j ≤ d}is equitable and its parameters do not depend on the edge xy. Let Γ be 1-homogeneous. Then Γ is distance-regular and also locally strongly regular with parameters (v′,k′,λ′,μ′), where v′ = k, k′ = a1, (v′ − k′ − 1)μ′ = k′(k′ − 1 − λ′) and c2 ≥ μ′ + 1, since a μ-graph is a regular graph with valency… Expand
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