Construction of directed strongly regular graphs using finite incidence structures

2010/06/28 by Oktay Ölmez, Olmez, O., Sung‐Yell Song +1
Computer Science · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.1006.5395

openalex publication_date 2010/06/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We use finite incident structures to construct new infinite families of directed strongly regular graphs with parameters (l(q-1)q^l, l(q-1)q^l-1, (lq-l+1)q^l-2, (l-1)(q-1)q^l-2, (lq-l+1)q^l-2) for integers q and l (q, l≥ 2), and (lq²(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 have parameters (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," at http://homepages.cwi.nl/^∼ aeb/math/dsrg/dsrg.html by S. Hobart and A. E. Brouwer. We 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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