File:Local mclaughlin graph.svg
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Contents
Summary
DescriptionLocal mclaughlin graph.svg |
English: 9-Sided symmetric embedding of Local McLaughlin Graph (162 vertices and 4536 edges). |
Date | |
Source | Own work |
Author | Claudio Rocchini |
Permission (Reusing this file) |
cc-by-3.0 |
Note
Many Thanks to nauty for autos.
Source Code
The complete C++ source code! Needs Nauty to find autos.
/***************************
* (C) 2010 Claudio Rocchini
* GPL License
***************************/
#include <stdio.h>
#include <math.h>
#include <vector>
#include <set>
#include <algorithm>
const double PI = 3.1415926535897932384626433832795;
typedef std::pair<int,int> edge;
static inline unsigned char f2b( double f ) {
if(f<0) f = 0; if(f>1) f = 1;
int i = int(f*256);
if(i>255) i = 255;
else if(i<0) i=0;
return i;
}
void HSV2RGB(double h, double s, double v, unsigned char rgb[3] ) {
if (s == 0) {
rgb[0] = rgb[1] = rgb[2] = f2b(v);
} else {
double v_h = h * 6;
double v_i = floor(v_h);
double v_1 = v * (1 - s);
double v_2 = v * (1 - s * (v_h - v_i));
double v_3 = v * (1 - s * (1 - (v_h - v_i)));
double v_r,v_g,v_b;
if (v_i == 0) {v_r = v; v_g = v_3; v_b = v_1;}
else if (v_i == 1) {v_r = v_2; v_g = v; v_b = v_1;}
else if (v_i == 2) {v_r = v_1; v_g = v; v_b = v_3;}
else if (v_i == 3) {v_r = v_1; v_g = v_2; v_b = v ;}
else if (v_i == 4) {v_r = v_3; v_g = v_1; v_b = v ;}
else {v_r = v; v_g = v_1; v_b = v_2;};
rgb[0] = f2b(v_r);
rgb[1] = f2b(v_g);
rgb[2] = f2b(v_b);
}
}
class permu
{
public:
std::vector<size_t> p;
void ident( size_t n ) {
p.resize(n); for(size_t i=0;i<n;++i) p[i] = i;
}
};
void copy( permu & dst, const permu & src ) {
dst.p.resize(src.p.size());
std::copy(src.p.begin(),src.p.end(),dst.p.begin());
}
void apply( permu & dst, const size_t perm[] ) {
permu t; copy(t,dst);
for(size_t i=0;i<dst.p.size();++i)
dst.p[i] = t.p[perm[i]];
}
void apply( permu & dst, const int perm[] ) {
permu t; copy(t,dst);
for(size_t i=0;i<dst.p.size();++i)
dst.p[i] = t.p[perm[i]];
}
bool operator== (const permu & a, const permu & b) {
std::vector<size_t>::const_iterator i,j;
for(i=a.p.begin(),j=b.p.begin();i!=a.p.end();++i,++j)
if(*i!=*j) return false;
return true;
}
bool operator< (const permu & a, const permu & b) {
std::vector<size_t>::const_iterator i,j;
for(i=a.p.begin(),j=b.p.begin();i!=a.p.end();++i,++j)
if(*i!=*j) return *i < *j;
return false;
}
size_t fix_point( const permu & pe ) {
size_t fix = 0;
for(size_t j=0;j<pe.p.size();++j)
if(pe.p[j]==j) ++fix;
return fix;
}
size_t cicle_size( const permu & pe ) {
permu t; copy(t,pe); size_t cs = 0;
for(;;) {
apply(t,& pe.p.front());
++cs; if(t==pe) break;
}
return cs;
}
size_t sub_loops( const permu & pe, std::vector< std::vector<size_t> > & loops ) {
std::vector<bool> done(pe.p.size()); std::fill(done.begin(),done.end(),false);
loops.clear();
for(;;) {
size_t i;
for(i=0;i<pe.p.size();++i) if(!done[i]) break;
if(i==pe.p.size()) break;
loops.push_back( std::vector<size_t>() );
size_t j = i;
do {
done[j] = true;
loops.back().push_back(j);
j = pe.p[j];
} while(j!=i);
}
return loops.size();
}
void out_nauty( int n, const std::vector<std::pair<int,int> > & edges, const char * filename) {
std::vector< std::vector<int> > vv;
vv.resize(n);
std::vector<std::pair<int,int> >::const_iterator i;
for(i=edges.begin();i!=edges.end();++i)
if((*i).first < (*i).second)
vv[(*i).first].push_back( (*i).second );
else
vv[(*i).second].push_back( (*i).first );
std::vector< std::vector<int> >::iterator j;
for(j=vv.begin();j!=vv.end();++j) std::sort(j->begin(),j->end());
FILE * fo = fopen(filename,"w");
fprintf(fo,"n=%d\ng\n",n);
for(j=vv.begin();j!=vv.end();++j) {
if(j!=vv.begin()) fprintf(fo,";\n");
std::vector<int>::iterator k;
for(k=j->begin();k!=j->end();++k) {
if(k!=j->begin()) fprintf(fo," ");
fprintf(fo,"%d",*k);
}
}
fprintf(fo,".\n");
fprintf(fo, "p\nx\no\nq\n");
fclose(fo);
}
void load_nauty( int NV, const char * filename, std::vector< std::vector<int> > & auto_base ) {
const int BSIZE = 1024; static char buff[1024];
auto_base.clear();
FILE * fp = fopen(filename,"r");
auto_base.push_back( std::vector<int>() );
while(fgets(buff,BSIZE,fp)){
if(strstr(buff,"grpsize"))
break;
else if(strstr(buff,"level"))
auto_base.push_back( std::vector<int>() );
else {
const char * sep = " \n\r\t"; char * p = strtok(buff,sep);
while(p){
if(auto_base.back().size()==size_t(NV))
auto_base.push_back( std::vector<int>() );
auto_base.back().push_back(atoi(p));
p = strtok(0,sep);
}
}
}
fclose(fp); auto_base.pop_back();
}
// n = master set size, m= subsets size
void make_subsets( int m, int n, std::vector< std::vector<int> > & subs ) {
std::vector<int> ss(m);
for(int i=0;i<m;++i) ss[i] = i;
subs.clear();
for(;;) {
subs.push_back( ss ); int i = m-1;
for(;;) {
if(++ss[i]<n) {
if(i==m-1) break;
ss[i+1]=ss[i]; ++i;
}
else if(--i<0) break;
}
if(i<0) break;
}
}
// number of commons element. a,b supposed ordered
int commons( std::vector<int> & a, std::vector<int> & b ) {
if(a.back()<b.front() || a.front()>b.back()) return 0;
int c = 0; std::vector<int>::const_iterator ia,ib;
for(ia=a.begin(),ib=b.begin();ia!=a.end() && ib!=b.end();) {
if(*ia==*ib) { ++c; ++ia; ++ib; }
else if(*ia<*ib) ++ia;
else ++ib;
}
return c;
}
// n = numero di caratteri, m = lunghezza stringhe, l=sotto-insiemi unici
void make_steiner_system( int l, int m, int n, std::vector< std::vector<int> > & out_blocks ) {
std::vector< std::vector<int> > blocks;
make_subsets(m,n,blocks);
size_t i,j;
std::vector<bool> oks(blocks.size());
std::fill(oks.begin(),oks.end(),true);
for(i=0;i<blocks.size()-1;++i) if(oks[i])
for(j=i+1;j<blocks.size();++j) if(oks[j])
if(commons(blocks[i],blocks[j])>=l) oks[j] = false;
out_blocks.clear();
for(i=0;i<blocks.size();++i) if(oks[i])
out_blocks.push_back( blocks[i] );
}
bool analyze_sym( int NV, permu & p, std::vector<int> & out_perm ) {
if(fix_point(p)!=0) return false;
size_t cs = cicle_size(p);
if(cs<4 || NV%cs!=0) return false;
std::vector< std::vector<size_t> > loops;
if(size_t(NV)==cs*loops.size()) {
std::vector< std::vector<size_t> >::iterator q;
size_t iq;
for(iq=0,q=loops.begin();q!=loops.end();++iq,++q) {
std::vector<size_t>::iterator w;
size_t iw;
for(iw=0,w=q->begin();w!=q->end();++iw,++w)
out_perm[ iq + loops.size()*iw ] = *w;
}
return true;
}
return false;
}
void find_symmetric( int NV, const std::vector< std::vector<int> > & auto_base, std::vector<int> & out_perm )
{
std::set<permu> perms;
std::vector<permu> active;
out_perm.resize(NV);
permu cu; cu.ident(NV);
perms.insert(cu); active.push_back(cu);
while(!active.empty()) {
std::vector<permu>::iterator i;
std::pair< std::set<permu>::iterator, bool > r;
std::vector<permu> old_active;
std::swap(old_active,active);
for(i=old_active.begin();i!=old_active.end();++i) {
for(size_t j=0;j<auto_base.size();++j) {
copy(cu,*i); apply(cu,&auto_base[j].front());
r = perms.insert(cu);
if(r.second) {
if(analyze_sym(NV,cu,out_perm)) return;
active.push_back(cu);
}
}
}
}
}
void save_svg_color( const char * filename, int NV, std::vector<edge> & edges, const int perm[] ) {
const double SX = 800; const double SY = 800;
const double RR = 2; const double BO = 10;
std::vector<double> px(NV); std::vector<double> py(NV);
FILE * fp = fopen(filename,"w");
fprintf(fp,
"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n"
"<svg\n"
"xmlns:svg=\"http://www.w3.org/2000/svg\"\n"
"xmlns=\"http://www.w3.org/2000/svg\"\n"
"version=\"1.0\"\n"
"width=\"%g\"\n" "height=\"%g\"\n"
"id=\"rockini\">\n"
,SX,SY
);
int i;
const double R = ((SX-BO*2)/2);
for(i=0;i<NV;++i) {
const double a = 2*PI*i/NV;
px[perm[i]] = SX/2 + R*cos(a);
py[perm[i]] = SY/2 + R*sin(a);
}
std::set<int> dist;
for(i=0;i<int(edges.size());++i) {
double dx = px[edges[i].first ] - px[edges[i].second];
double dy = py[edges[i].first ] - py[edges[i].second];
int di = int(sqrt(dx*dx+dy*dy)+0.5);
dist.insert(di);
}
std::vector<int> vdist;
std::set<int>::iterator id;
for(id=dist.begin();id!=dist.end();++id)
vdist.push_back(*id);
for(size_t co=0;co<vdist.size();++co) {
unsigned char rgb[3];
HSV2RGB(double(co)*2/(3*vdist.size()),0.9,0.8,rgb);
fprintf(fp,"<g id=\"edges\" style=\"stroke:#%02X%02X%02X;stroke-width:0.1;\">\n",
rgb[0],rgb[1],rgb[2]);
for(i=0;i<int(edges.size());++i) {
double dx = px[edges[i].first ] - px[edges[i].second];
double dy = py[edges[i].first ] - py[edges[i].second];
int di = int(sqrt(dx*dx+dy*dy)+0.5);
if(di!=vdist[co]) continue;
fprintf(fp,
"<line x1=\"%5.1lf\" y1=\"%5.1lf\" x2=\"%5.1lf\" y2=\"%5.1lf\"/>\n"
,px[edges[i].first ],py[edges[i].first ]
,px[edges[i].second],py[edges[i].second]
);
}
fprintf(fp,"</g>\n");
}
fprintf(fp,"<g id=\"nodes\" style=\"stroke:#000000;stroke-width:1;stroke-opacity:1.0;fill:#040000\">\n");
for(i=0;i<NV;++i)
fprintf(fp,"<circle cx=\"%5.1lf\" cy=\"%5.1lf\" r=\"%5.1lf\"/>\n",px[i],py[i],RR);
fprintf(fp,"</g>\n");
fprintf(fp,"</svg>\n");
fclose(fp);
}
int main(){
size_t i,j,k,h;
// Make McLaughlin Graph
const int NVMC = 275; // 22=steiner char >0, 77 = B blocks contains 0, 176 = C block not-contains
std::vector< std::vector<int> > blocks;
make_steiner_system(4,7,23,blocks);
std::vector<size_t> B; std::vector<size_t> C;
for(i=0;i<blocks.size();++i)
if(std::find(blocks[i].begin(),blocks[i].end(),0)!=blocks[i].end())
B.push_back(i);
else C.push_back(i);
std::vector<edge> edges_mc;
for(i=0;i<22;++i) for(j=0;j<B.size();++j) {
k = B[j];
if(std::find(blocks[k].begin(),blocks[k].end(),i+1)==blocks[k].end())
edges_mc.push_back( edge(i,j+22) );
}
for(i=0;i<B.size()-1;++i) for(j=i+1;j<B.size();++j)
if(commons(blocks[B[i]],blocks[B[j]])==1)
edges_mc.push_back( edge(i+22,j+22) );
for(i=0;i<22;++i) for(j=0;j<C.size();++j) {
k = C[j];
if(std::find(blocks[k].begin(),blocks[k].end(),i+1)!=blocks[k].end())
edges_mc.push_back( edge(i,j+99) );
}
for(i=0;i<B.size();++i) {
k = B[i];
for(j=0;j<C.size();++j) {
h = C[j];
if(commons(blocks[k],blocks[h])==3)
edges_mc.push_back( edge(i+22,j+99) );
}
}
for(i=0;i<C.size()-1;++i) for(j=i+1;j<C.size();++j)
if(commons(blocks[C[i]],blocks[C[j]])==1)
edges_mc.push_back( edge(i+99,j+99) );
// Make Local McLaughlin Graph
std::vector<bool> deleted(NVMC); std::fill(deleted.begin(),deleted.end(),false);
deleted[0] = true;
std::vector<edge>::iterator ie;
for(ie=edges_mc.begin();ie!=edges_mc.end();++ie) {
if((*ie).first==0) deleted[(*ie).second] = true;
if((*ie).second==0) deleted[(*ie).first] = true;
}
size_t NV = 0; std::vector<int> reindex(NVMC);
for(i=0;i<deleted.size();++i)
if(!deleted[i]) reindex[i] = NV++;
else reindex[i] = -1;
printf("%u vertices\n",NV);
std::vector<edge> edges;
for(ie=edges_mc.begin();ie!=edges_mc.end();++ie) {
int rf = reindex[(*ie).first];
int rs = reindex[(*ie).second];
if(rf!=-1 && rs!=-1) edges.push_back( edge(rf,rs) );
}
printf("%u edges\n",edges.size());
// nauty
out_nauty(NV,edges,"lmclaughlin_i.txt");
system("nauty < lmclaughlin_i.txt > lmclaughlin_o.txt");
std::vector< std::vector<int> > auto_base;
load_nauty(NV,"lmclaughlin_o.txt",auto_base);
std::vector<int> out_perm;
find_symmetric(NV,auto_base,out_perm);
save_svg_color("c:\\temp\\lmclaughlin.svg",NV,edges,&out_perm.front());
return 0;
}
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- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 06:55, 30 September 2010 | ![]() | 800 × 800 (248 KB) | Rocchini | stroke-width increased |
08:43, 9 July 2010 | ![]() | 800 × 800 (248 KB) | Rocchini | {{Information |Description={{en|1=9-Sided symmetric embedding of Local McLaughlin Graph (162 vertices and 4536 edges).}} |Source={{own}} |Author=Rocchini |Date=2010-07-09 |Permission=cc-by-3.0 |other_versions= }} |
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