File:Local mclaughlin graph.svg

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Summary

DescriptionLocal mclaughlin graph.svg	English: 9-Sided symmetric embedding of Local McLaughlin Graph (162 vertices and 4536 edges).
Date	9 July 2010
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;
}

Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:

This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.

You are free:

to share – to copy, distribute and transmit the work
to remix – to adapt the work

Under the following conditions:

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.
share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

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.

You may select the license of your choice.

File history

Click on a date/time to view the file as it appeared at that time.

	Date/Time	Thumbnail	Dimensions	User	Comment
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= }}

File usage

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- Потребител:Stanqo/Математика
Usage on es.wikipedia.org
- Anexo:Galería de grafos
Usage on fr.wikipedia.org
- Graphe local de McLaughlin
Usage on ja.wikipedia.org
- 名称のあるグラフのギャラリー
Usage on www.wikidata.org
- Q3115586
- User:AVDLCZ/List of graphs

File:Local mclaughlin graph.svg

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copyright license

GNU Free Documentation License, version 1.2 or later

Creative Commons Attribution-ShareAlike 3.0 Unported

source of file

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9 July 2010

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