On Wednesday, October 19, 2016 at 7:05:23 AM UTC+1, ywr nn wrote: > > hi, Dima! > > 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 > [(q+1)^(q^2), q^(q+1)]. > 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? >
Well, as I said, it was also discovered simultaneously and independently by Erdós and Rényi (see e.g. http://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i2p21/pdf for a short discussion on this) Does this sound right to you? Dima > yawara > > On Mon, Oct 10, 2016 at 8:52 PM, Dima Pasechnik <dim...@gmail.com > <javascript:>> 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. >>> http://www.emis.ams.org/journals/EJC/Surveys/ds14.pdf >>> >>> 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, >> IMHO. >> >> 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 :-) >> https://www.cs.ox.ac.uk/publications/publication7266-abstract.html >> >> Please feel free to cc me on the Sage ticket with an implementation, I'd >> be glad to review it. >> >> Dima >> >> >>> If not, I plan to implement it for sagemath. >>> >>> yawara >>> >> -- >> You received this message because you are subscribed to the Google Groups >> "sage-devel" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to sage-devel+...@googlegroups.com <javascript:>. >> To post to this group, send email to sage-...@googlegroups.com >> <javascript:>. >> Visit this group at https://groups.google.com/group/sage-devel. >> For more options, visit https://groups.google.com/d/optout. >> > > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
