In my context, for every power of primes q, Brown's construction gives a
graph with order q^2+q+1, maximum degree q+1, diameter 2.
The graph is not a regular one. The degree sequence of the graph is
This Brown's construction gives known largest lower bounds for the
degree-diameter problem for the case of diameter 2.
Is not this construction called "Brown's construction" in graph theory?
On Mon, Oct 10, 2016 at 8:52 PM, Dima Pasechnik <dimp...@gmail.com> wrote:
> On Sunday, October 9, 2016 at 9:10:50 PM UTC, ni732...@gmail.com wrote:
>> Brown's construction is the function which takes a finite field to a
>> graph with diameter 2.
>> Is it available in the graph component of sagemath?
> I won't be surprised if it could be constructed as a subgraph of one of
> many strongly regular graphs
> known to Sage, but there is no direct way to build such a graph in Sage,
> The description of the adjacency in the link you provide is a bit too
> brief to see what exactly it does,
> but I think these graphs are also known as Erdős–Rényi graphs, from
> P. Erdós, A. Rényi, V.T. Sós
> On a problem of graph theory
> Studia Sci. Math. Hungar., 1 (1966), pp. 215–235
> Brown's paper was published in the same year: W.G. Brown
> On graphs that do not contain a Thomsen graph
> Canad. Math. Bull., 9 (1966), pp. 281–285
> We published a paper where these graphs were considered, and I implemented
> a construction of them in GAP, but not in Sage :-)
> Please feel free to cc me on the Sage ticket with an implementation, I'd
> be glad to review it.
>> If not, I plan to implement it for sagemath.
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