Construction of Directed Strongly Regular Graphs Using Finite Incidence Structures
نویسندگان
چکیده
We use finite incident structures to construct new infinite families of directed strongly regular graphs with parameters (l(q−1)q, l(q−1)q, (lq−l+1)q, (l−1)(q−1)q, (lq−l+1)q) for integers q and l (q, l ≥ 2), and (lq(q − 1), lq(q − 1), lq − l + 1, (l − 1)(q − 1), lq − l + 1) for all prime powers q and l ∈ {1, 2, . . . , q}. The new graphs given by these constructions include those with parameter sets (36, 12, 5, 2, 5), (54, 18, 7, 4, 7), (72, 24, 10, 4, 10), (96, 24, 7, 3, 7), (108, 36, 14, 8, 14) and (108, 36, 15, 6, 15) listed as feasible parameters on “Parameters of directed strongly regular graphs” by S. Hobart and A. E. Brouwer at http : //homepages.cwi.nl/∼aeb/math/dsrg/dsrg.html. We also review these constructions and show how our methods may be used to construct other infinite families of directed strongly regular graphs.
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