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A directed graph version of strongly regular graphs. (English) Zbl 0642.05025
The paper gives existence and nonexistence conditions of a directed graph version of strongly regular graphs whose adjacency matrices satisfy the equations \[ A^ 2+(u-v)A-(t-u)I=uJ\quad \] \[ AJ=JA=kJ \] where A is the adjacency matrix, I the identity matrix, J the matrix of all l’s and u, v, t, k are the parameters. It proves the existence by construction and also constructs homomorphisms for several families of parameter sets.
Reviewer: Wai-Kai Chen

MSC:
05C20 Directed graphs (digraphs), tournaments
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
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