The Subconstituent Algebra of a Strongly Regular Graph

The subconstituent algebra of a bipartite distance-regular graph; thin modules with endpoint two

We consider a bipartite distance-regular graph Γ with diameter D ≥ 4, valency k ≥ 3, intersection numbers bi, ci, distance matrices Ai, and eigenvalues θ0 > θ1 > · · · > θD. Let X denote the vertex set of Γ and fix x ∈ X. Let T = T (x) denote the subalgebra of MatX(C) generated by A,E ∗ 0 , E ∗ 1 , . . . , E ∗ D, where A = A1 and E ∗ i denotes the projection onto the i th subconstituent of Γ wi...

Taut distance-regular graphs and the subconstituent algebra

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 X̆ = {y ∈ X | ∂(x, y) = 2}, and edge set R̆ = {yz | y, z ∈ X̆, ∂(y, z) = 2}, where ∂ is the path-length distance function for Γ. The graph Γ22 has exactly k2 vertices, where k2 is the second valency of Γ. Let η1, η2, . . . ...

On the Strongly Regular Graph of Parameters

In an attempt to find a strongly regular graph of parameters (99, 14, 1, 2) or to disprove its existence, we studied its possible substructure and constructions.

The Maximum Number of Edges in a Strongly Multiplicative Graph

Feasibility Conditions on the Parameters of a Strongly Regular Graph

We consider a strongly regular graph, G, and associate a three dimensional Euclidean Jordan algebra, V, to the adjacency matrix A of G. Then, by considering convergent series of Hadamard powers of the idempotents of the unique complete system of orthogonal idempotents of V, we establish new feasibility conditions for the existence of strongly regular graphs.