strongly regular tournaments

[dimpase]

This is a followup to #24045:

This is generalisation of Paley digraphs from #24045, due to A.Duval, ​J.Comb.Th. 47(1988) pp. 71-100, nowadays called strongly regular digraph/tournament. We can use code in comment 14 of #24045, and Paley would be a subcase (in fact, this code will give you Paley if 4n-1 happens to be a prime power).

Component: graph theory

Author: Matteo Cati

Issue created by migration from https://trac.sagemath.org/ticket/24682

[MatteoCati]

Author: Matteo Cati

[MatteoCati]

Commit: 4cd5664

[MatteoCati]

New commits:

4cd5664

Add construction of strongly regular digraph

[MatteoCati]

Branch: u/gh-MatteoCati/add_strongly_regular_digraph

[dcoudert]

comment:3

You assume the existence of a unique strongly regular digraph of order n. Is it the case ?

• n+1 -> n + 1
• f'Strongly regular digraph' -> 'Strongly regular digraph'

[dimpase]

comment:4

no, they are usually not unique (IIRC, already for 19 nodes it's not the case)

[dimpase]

comment:5

But where do you see a uniqueness promise? The docs say

Return a Strongly Regular digraph with `n` vertices.`

[dcoudert]

comment:6

I haven't seen any promise on the uniqueness. I just observed that the construction always returns the same digraph of order n.
You could add in the documentation for future work to add other constructions.

[dimpase]

comment:7

yes, it's the same for many other combinatorics and graphs constructions.
E.g. if you ask for a Hadamard matrix of order n you get the 1st found, or if you ask got a strongly regular graph with the given parameters you get the 1st founds, same for block designs, orthogonal arrays, etc.

(the trac is read-only for all, except me, now, we'll get back to this on GitHub :-))

[dimpase]

comment:8

test+1

[mkoeppe]

Removed branch from the issue description because it has been replaced by PR #34986