I just got it wrong. I understand what you said and will implement Erdos-Renyi graph for sage.
Where can I read your GAP code? I want to read it for study. yawara On Wednesday, October 19, 2016 at 11:29:27 PM UTC+9, Dima Pasechnik wrote: > > > > 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> 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. >>> To post to this group, send email to sage-...@googlegroups.com. >>> 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.
