论文信息 - A directed graph version of strongly regular graphs

A directed graph version of strongly regular graphs

We study a directed graph version of strongly regular graphs whose adjacency matrices satisfy A^2 + (μ − λ)A − (t − μ)I = μJ, and AJ = JA = kJ. We prove existence (by construction), nonexistence, and necessary conditions, and construct homomorphisms for several families of parameter sets.

Art M. Duval

[1] B. Bollobás. Surveys in Combinatorics , 1979 .

[2] A. J. Hoffman,et al. On the Uniqueness of the Triangular Association Scheme , 1960 .

[3] William Bridges,et al. The polynomial of a non-regular digraph , 1971 .

[4] Jacobus H. van Lint,et al. Directed graphs with unique paths of fixed length , 1978, J. Comb. Theory, Ser. B.

[5] Clement W. H. Lam. A Generalization of Cyclic Difference Sets II , 1975, J. Comb. Theory, Ser. A.

[6] Clement W. H. Lam,et al. On Some Solutions of Ak = dl + lambda J , 1977, J. Comb. Theory, Ser. A.

[7] H. J. Ryser. A generalization of the matrix equation A2 = J☆ , 1970 .

[8] W. G. Bridges,et al. X k -Digraphs. , 1981 .

[9] S. S. Shrikhande. On a Characterization of the Triangular Association Scheme , 1959 .

[10] Alan J. Hoffman,et al. On Moore Graphs with Diameters 2 and 3 , 1960, IBM J. Res. Dev..