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October 20, 2025Open Access

Explicit construction of infinite families of strongly regular digraphs with parameters ( (v+ (2^n+1-4) t) 2^n-1, k+ (2ⁿ-2) t, t, λ, t)

Key Points

Strongly regular digraphs with newly defined parameters were constructed, expanding existing knowledge.
A computer program identified initial digraphs, forming the basis for further parameter sequences.
The approach successfully produced 11 distinct families of strongly regular digraphs with varied characteristics.
This work addresses previously open questions about the existence of specific digraph families.

Abstract

An explicit construction of infinite sequences of strongly regular digraphs with parameter sets ( (v+ (2^n+1-4) t) 2^n-1, k+ (2ⁿ-2) t, t, λ, t) is described. A computer program was used to find the initial digraphs. The remaining terms of the sequence are obtained by the constructed recurrence. Using the described approach, 11 families of strongly regular digraphs were found. In particular, these families contain digraphs dsrg (72, 18, 5, 3, 5), dsrg (76, 19, 5, 4, 5), dsrg (92, 23, 6, 5, 6) and dsrg (104, 26, 7, 5, 7), the question of the existence of which was previously open.

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