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genspecialg.c
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/* genspecialg.c version 2.1; B D McKay, June 14, 2023 */
#define USAGE \
"genspecialg [-s|-g|-z|-d|-v] [-q] [graph options]... [outfile]"
#define HELPTEXT \
" Generate special graphs.\n\
# : size parameter called n in the descriptions\n\
\n\
-s : Write in sparse6 format (default)\n\
-g : Write in graph6 format\n\
-z : Make digraph versions and write in digraph6 format\n\
-d : Write in dreadnaut format (can be used with -z)\n\
-v : For each graph, report the size to stderr\n\
-q : Suppress summary\n\
\n\
If defined, the digraph version is shown in parentheses:\n\
-p# : path (directed path) on n vertices\n\
-c# : cycle (directed cycle) on n vertices\n\
-e# : empty graph (digraph with loops only) on n vertices\n\
-k# : complete graph (with loops) on n vertices\n\
-b#,#[,#] : complete bipartite graph (directed l->r) on n vertices\n\
minus a matching of given size if present\n\
-m#,#... : multipartite graph\n\
-a# : antiprism (directed antiprism) on 2n\n\
-l# : moebius ladder (directed cycle, undirected rungs) with # vertices\n\
-D#,# : de Bruijn graph (digraph). D(m,t) has order m^t\n\
-w# : wheel with # spokes (directed out from hub)\n\
-f# : flower snark on 4n vertices\n\
-L# : triangular graph, the linegraph of K_n\n\
-P#,# : generalized Petersen graph; usual one is -P5,2\n\
-Q# -Q#,# : hypercube on 2^n vertices. Q(n,t) has vertices {0,1}^n\n\
and edges for hamming distance t. t=1 is default.\n\
-A# : connected antiregular graph on n vertices\n\
-J#,# : Johnson graph J(n,k), args are n and k\n\
-K#,# -K#,#,# : Generalized Kneser graph. K(n,k,t) is graph of k-subsets\n\
of an n-set whose intersection is t. Default for t is 0.\n\
-C#,#... : circulant (di)graph; first arg is the number of vertices\n\
-T#,#... : theta (di)graph Theta(#,#,...), give path lengths\n\
-G#,#... : (directed) grid, use negative values for open directions\n\
-Y# : Paley graph or digraph, depending on size. Nondeterministic.\n\
-X# : produce a named graph, # can be an index or a partial name.\n\
Use genspecialg --Xhelp for a list.\n\
\n\
Any number of graphs can be generated at once.\n"
/* Ideas: full trees, friendship, chess graphs,
double wheels, books, Blanusa snarks. */
#include "gtools.h"
#include "namedgraphs.h"
#define MAXARGS 10000 /* Maximum argument list for multi-argument parameters */
#define SWAP(x,y) {int w = x; x = y; y = w;}
static long args[MAXARGS];
static short vmark_val = 32000;
DYNALLSTAT(short,vmark,vmark_sz);
#define MARK(i) vmark[i] = vmark_val
#define UNMARK(i) vmark[i] = 0
#define ISMARKED(i) (vmark[i] == vmark_val)
#define ISNOTMARKED(i) (vmark[i] != vmark_val)
#define RESETMARKS {if (vmark_val++ >= 32000) \
{size_t ij; for (ij=0;ij<vmark_sz;++ij) vmark[ij]=0; vmark_val=1;}}
static void
preparemarks(size_t nn)
{
size_t oldsize;
short *oldpos;
oldsize = vmark_sz;
oldpos = vmark;
DYNALLOC1(short,vmark,vmark_sz,nn,"preparemarks");
if (vmark_sz != oldsize || vmark != oldpos) vmark_val = 32000;
}
/**************************************************************************/
static void
writedread_sg(FILE *f, sparsegraph *sg, boolean digraph)
/* Write in dreadnaut format */
{
size_t *v;
int *d,*e,n,i,j,k;
SG_VDE(sg,v,d,e);
n = sg->nv;
if (digraph) fprintf(f,"n=%d $=0 dg\n",n);
else fprintf(f,"n=%d $=0 g\n",n);
for (i = 0; i < n; ++i)
{
for (j = 0; j < d[i]; ++j)
{
k = e[v[i]+j];
if (k >= i || digraph) fprintf(f," %d",k);
}
if (i == n-1) fprintf(f,".\n$$\n");
else fprintf(f,";\n");
}
}
static void
writedread(FILE *f, graph *g, boolean digraph, int m, int n)
/* Write in dreadnaut format */
{
int i,j;
graph *gi;
if (digraph) fprintf(f,"n=%d $=0 dg\n",n);
else fprintf(f,"n=%d $=0 g\n",n);
for (i = 0, gi = g; i < n; ++i, gi += m)
{
for (j = (digraph ? -1 : i-1) ; (j = nextelement(gi,m,j)) >= 0; )
fprintf(f," %d",j);
if (i == n-1) fprintf(f,".\n$$\n");
else fprintf(f,";\n");
}
}
/**************************************************************************/
static int binom[32][16]; /* Cached binomial coefficients */
static int
binomial(int n, int k)
/* Value of binomial(n,k), error if too big for int */
{
int i,nki,ans;
nauty_counter work;
if (k > n/2) k = n - k;
if (k < 0) return 0;
if (n < 32 && binom[n][k] > 0) return binom[n][k];
work = 1;
for (i = 1; i <= k; ++i)
{
nki = n-k+i;
work = (work/i) * nki + (work%i) * nki / i;
if ((int)work != work) { fprintf(stderr,"Overflow\n"); exit(1); }
}
ans = (int)work;
if (n < 32) binom[n][k] = ans;
return ans;
}
/**************************************************************************/
static void
unrank(int r, int k, int *a)
/* r-th k-set in colex order (r=0,1,...) */
{
int i,p;
for (i = k; i > 0; --i)
{
p = i - 1;
do ++p; while (binomial(p,i) <= r);
r -= binomial(p-1,i);
a[i-1] = p-1;
}
}
static int
rank(int k, int *a)
/* Rank of a[0..k-1] in colex order */
{
int i,r;
r = 0;
for (i = 0; i < k; ++i)
r += binomial(a[i],i+1);
return r;
}
/**************************************************************************/
static int
vnumber(long *dimen, int *index, int ndimen)
{
int i,v;
v = 0;
for (i = 0; i < ndimen; ++i)
v = v*dimen[i] + index[i];
return v;
}
/**************************************************************************/
static void
makepath(long n, boolean digraph, sparsegraph *sg)
{
int *d,*e,i;
size_t *v,k;
if (n < 1 || n > NAUTY_INFINITY-2)
gt_abort(">E genspecialg: bad argument for -p\n");
if (digraph) SG_ALLOC(*sg,n,n-1,"genspecialg");
else SG_ALLOC(*sg,n,2*(size_t)n-2,"genspecialg");
SG_VDE(sg,v,d,e);
if (digraph || n == 1)
{
sg->nv = n;
sg->nde = n-1;
for (i = 0; i < n-1; ++i)
{
d[i] = 1;
v[i] = i;
e[i] = i+1;
}
d[n-1] = 0;
v[n-1] = 0;
}
else
{
sg->nv = n;
sg->nde = 2*(size_t)n-2;
d[0] = 1;
v[0] = 0;
e[0] = 1;
for (i = 1, k = 1; i < n-1; ++i, k += 2)
{
d[i] = 2;
v[i] = k;
e[k] = i-1;
e[k+1] = i+1;
}
d[n-1] = 1;
v[n-1] = k;
e[k] = n-2;
}
}
/**************************************************************************/
static void
makecycle(long n, boolean digraph, sparsegraph *sg)
{
int *d,*e,i;
size_t *v;
if (!digraph && (n < 1 || n == 2 || n > NAUTY_INFINITY-2))
gt_abort(">E genspecialg: bad argument for -c\n");
if (digraph && (n < 1 || n > NAUTY_INFINITY-2))
gt_abort(">E genspecialg: bad argument for -zc\n");
if (digraph) SG_ALLOC(*sg,n,n,"genspecialg");
else SG_ALLOC(*sg,n,2*(size_t)n,"genspecialg");
SG_VDE(sg,v,d,e);
if (digraph || n == 1)
{
sg->nv = n;
sg->nde = n;
for (i = 0; i < n-1; ++i)
{
d[i] = 1;
v[i] = i;
e[i] = i+1;
}
d[n-1] = 1;
v[n-1] = n-1;
e[n-1] = 0;
}
else
{
sg->nv = n;
sg->nde = 2*(size_t)n;
d[0] = 2;
v[0] = 0;
e[0] = 1;
e[1] = n-1;
for (i = 1; i < n-1; ++i)
{
d[i] = 2;
v[i] = 2*(size_t)i;
e[2*(size_t)i] = i-1;
e[2*(size_t)i+1] = i+1;
}
d[n-1] = 2;
v[n-1] = 2*(size_t)n-2;
e[2UL*n-2] = 0;
e[2UL*n-1] = n-2;
}
}
/**************************************************************************/
static void
makewheel(long k, boolean digraph, sparsegraph *sg)
/* Make a wheel with k spokes. In the directed version, spokes
are oriented out from the hub. */
{
int n,*d,*e,i;
size_t *v,nde;
if (k < 3 || k > NAUTY_INFINITY-3)
gt_abort(">E genspecialg: bad argument for -w\n");
n = k+1;
if (digraph) nde = 2*(size_t)k;
else nde = 4*(size_t)k;
SG_ALLOC(*sg,n,nde,"genspecialg");
SG_VDE(sg,v,d,e);
sg->nv = n;
sg->nde = nde;
if (digraph)
{
d[0] = n-1;
v[0] = 0;
for (i = 1; i < n; ++i)
{
d[i] = 1;
v[i] = k+i-1;
}
for (i = 1; i < n; ++i)
{
e[v[0]+i-1] = i;
e[v[i]] = (i == n-1 ? 1 : i+1);
}
}
else
{
d[0] = n-1;
v[0] = 0;
for (i = 1; i < n; ++i)
{
d[i] = 3;
v[i] = k+3*(size_t)i-3;
}
for (i = 1; i < n; ++i)
{
e[v[0]+i-1] = i;
e[v[i]] = 0;
e[v[i]+1] = (i == n-1 ? 1 : i+1);
e[v[i]+2] = (i == 1 ? n-1 : i-1);
}
}
}
/**************************************************************************/
static void
makedebruijngraph(long k, long t, boolean digraph, sparsegraph *sg)
/* Make a de Bruijn graph or digraph for words of length t over
an alphabet of size k. */
{
int *d,*e,i,j,n,nok;
int jn,ki,di;
size_t *v,nde;
long l0,l1;
if (k < 2 || t < 2)
gt_abort(">E genspecialg: bad arguments for -D\n");
l0 = 1;
for (i = 0; i < t; ++i)
{
l1 = l0 * k;
if (l1 / k != l0)
gt_abort(">E genspecialg: too many vertices for -D\n");
l0 = l1;
}
if (l0 > NAUTY_INFINITY-2)
gt_abort(">E genspecialg: too many vertices for -D\n");
n = l0;
nok = n / k;
if (digraph) nde = n*(size_t)k;
else nde = 2*(size_t)n*k; /* upper bound, what is the real number? */
SG_ALLOC(*sg,n,nde,"genspecialg");
SG_VDE(sg,v,d,e);
sg->nv = n;
sg->nde = nde;
if (digraph)
{
for (i = 0; i < n; ++i)
{
d[i] = k;
v[i] = i*(size_t)k;
ki = k * (i%nok);
for (j = 0; j < k; ++j)
e[v[i]+j] = ki + j;
}
}
else
{
for (i = 0; i < n; ++i)
{
di = 0;
v[i] = (i == 0 ? 0 : v[i-1] + d[i-1]);
ki = k * (i%nok);
for (j = 0; j < k; ++j)
{
e[v[i]+di] = ki + j;
++di;
jn = (i/k) + j*nok;
if (jn / k != i % nok)
{
e[v[i]+di] = jn;
++di;
}
}
d[i] = di;
}
sg->nde = v[n-1]+d[n-1];
}
}
/**************************************************************************/
static void
makemoebiusladder(long k, boolean digraph, sparsegraph *sg)
/* Make a Moebius ladder with k vertices (k even).
This is the same as a cycle with diagonal rungs.
In the directed version only the cycle is directed. */
{
int n,*d,*e,i;
size_t *v,nde;
if (k < 3 || k % 2 != 0 || k > NAUTY_INFINITY-2)
gt_abort(">E genspecialg: bad argument for -l\n");
n = k;
if (digraph) nde = 2*(size_t)k;
else nde = 3*(size_t)k;
SG_ALLOC(*sg,n,nde,"genspecialg");
SG_VDE(sg,v,d,e);
sg->nv = n;
sg->nde = nde;
if (digraph)
{
for (i = 0; i < n; ++i) d[i] = 2;
for (i = 0; i < n; ++i) v[i] = 2*(size_t)i;
for (i = 0; i < n; ++i) e[v[i]] = (i==n-1 ? 0 : i+1);
for (i = 0; i < n/2; ++i)
{
e[v[i]+1] = i + n/2;
e[v[i+n/2]+1] = i;
}
}
else
{
for (i = 0; i < n; ++i) d[i] = 3;
for (i = 0; i < n; ++i) v[i] = 3*(size_t)i;
for (i = 0; i < n; ++i) e[v[i]] = (i==n-1 ? 0 : i+1);
for (i = 0; i < n; ++i) e[v[i]+1] = (i==0 ? n-1 : i-1);
for (i = 0; i < n/2; ++i)
{
e[v[i]+2] = i + n/2;
e[v[i+n/2]+2] = i;
}
}
}
/**************************************************************************/
static void
makeantiprism(long k, boolean digraph, sparsegraph *sg)
/* Make an antiprism with 2*k vertices.
The directed version has the rungs oriented in the same
sense as the cycles.
*/
{
int n,*d,*e,i;
size_t *v,nde;
if (k < 3 || k > (NAUTY_INFINITY-2)/2)
gt_abort(">E genspecialg: bad argument for -a\n");
n = 2*k;
if (digraph) nde = 4*(size_t)k;
else nde = 8*(size_t)k;
SG_ALLOC(*sg,n,nde,"genspecialg");
SG_VDE(sg,v,d,e);
sg->nv = n;
sg->nde = nde;
if (digraph)
{
for (i = 0; i < n; ++i)
{
d[i] = 2;
v[i] = 2*(size_t)i;
}
for (i = 0; i < k; ++i)
{
e[v[i]] = (i == k-1 ? 0 : i+1);
e[v[i]+1] = k + i;
}
for (i = k; i < n; ++i)
{
e[v[i]] = (i == n-1 ? k : i+1);
e[v[i]+1] = (i == n-1 ? 0 : i-k+1);
}
}
else
{
for (i = 0; i < n; ++i)
{
d[i] = 4;
v[i] = 4*(size_t)i;
}
for (i = 0; i < k; ++i)
{
e[v[i]] = (i == k-1 ? 0 : i+1);
e[v[i]+1] = (i == 0 ? k-1 : i-1);
e[v[i]+2] = k + i;
e[v[i]+3] = (i == 0 ? n-1 : i+k-1);
}
for (i = k; i < n; ++i)
{
e[v[i]] = (i == n-1 ? k : i+1);
e[v[i]+1] = (i == k ? n-1 : i-1);
e[v[i]+2] = i - k;
e[v[i]+3] = (i == n-1 ? 0 : i-k+1);
}
}
}
/**************************************************************************/
static void
makeflowersnark(long k, boolean digraph, sparsegraph *sg)
/* Flower snark on 4*k vertices, no digraph variant
*
* The flower snark Jn can be constructed with the following process :
* Build n copies of the star graph on 4 vertices. Denote the
* central vertex of each star Ai and the outer vertices Bi, Ci and
* Di. This results in a disconnected graph on 4n vertices with 3n
* edges (Ai-Bi, Ai-Ci and Ai-Di for 1?i?n). Construct the n-cycle
* (B1... Bn). This adds n edges. Finally construct the 2n-cycle
* (C1... CnD1... Dn). This adds 2n edges. By construction, the
* Flower snark Jn is a cubic graph with 4n vertices and 6n edges.
*/
#define FSA(i) (4*(i))
#define FSB(i) (4*(i)+1)
#define FSC(i) (4*(i)+2)
#define FSD(i) (4*(i)+3)
{
int n,*d,*e,i,j;
size_t *v,nde;
if (k < 3 || k > (NAUTY_INFINITY-2)/4)
gt_abort(">E genspecialg: bad argument for -f\n");
n = 4*k;
nde = 12*(size_t)k;
SG_ALLOC(*sg,n,nde,"genspecialg");
SG_VDE(sg,v,d,e);
sg->nv = n;
sg->nde = nde;
for (i = 0; i < n; ++i)
{
d[i] = 0;
v[i] = 3*(size_t)i;
}
for (i = 0; i < k; ++i)
{
e[v[FSA(i)]+d[FSA(i)]++] = FSB(i);
e[v[FSB(i)]+d[FSB(i)]++] = FSA(i);
e[v[FSA(i)]+d[FSA(i)]++] = FSC(i);
e[v[FSC(i)]+d[FSC(i)]++] = FSA(i);
e[v[FSA(i)]+d[FSA(i)]++] = FSD(i);
e[v[FSD(i)]+d[FSD(i)]++] = FSA(i);
}
for (i = 0; i < k; ++i)
{
j = FSB((i+1)%k);
e[v[FSB(i)]+d[FSB(i)]++] = j;
e[v[j]+d[j]++] = FSB(i);
}
for (i = 0; i < k-1; ++i)
{
e[v[FSC(i)]+d[FSC(i)]++] = FSC(i+1);
e[v[FSC(i+1)]+d[FSC(i+1)]++] = FSC(i);
}
for (i = 0; i < k-1; ++i)
{
e[v[FSD(i)]+d[FSD(i)]++] = FSD(i+1);
e[v[FSD(i+1)]+d[FSD(i+1)]++] = FSD(i);
}
e[v[FSD(0)]+d[FSD(0)]++] = FSC(k-1);
e[v[FSC(k-1)]+d[FSC(k-1)]++] = FSD(0);
e[v[FSC(0)]+d[FSC(0)]++] = FSD(k-1);
e[v[FSD(k-1)]+d[FSD(k-1)]++] = FSC(0);
}
static void
maketriangular(long k, boolean digraph, sparsegraph *sg)
/* Triangular graph on k(k-1)/2 vertices, no digraph variant
*/
#define DIRPAIR(i,j) ((j)+(i)*k-((i)+1)*((i)+2)/2)
#define PAIR(i,j) ((i)<(j) ? DIRPAIR(i,j) : DIRPAIR(j,i))
{
int n,*d,*e,*vx,i,j,t;
size_t *v,nde,deg;
if (k < 2 || k*(k-1)/2 > NAUTY_INFINITY-2)
gt_abort(">E genspecialg: bad argument for -L\n");
n = k*(k-1)/2;
deg = 2*(k-2);
nde = deg*(size_t)n;
SG_ALLOC(*sg,n,nde,"genspecialg");
SG_VDE(sg,v,d,e);
sg->nv = n;
sg->nde = nde;
for (i = 0; i < n; ++i)
{
d[i] = deg;
v[i] = deg*(size_t)i;
}
for (i = 0; i < k-1; ++i)
for (j = i+1; j < k; ++j)
{
vx = e + v[PAIR(i,j)];
for (t = 0; t < k; ++t)
{
if (t != i && t != j)
{
*(vx++) = PAIR(i,t);
*(vx++) = PAIR(j,t);
}
}
}
}
/**************************************************************************/
static void
makeJohnson(long n, long k, boolean digraph, sparsegraph *sg)
{
size_t *v;
int *d,*e,*ep,nv,deg,i,j,s,t,u;
int *a,*b;
if (k > n/2) k = n - k;
if (k < 0) gt_abort(">E genspecialg: bad parameters for -J\n");
nv = binomial(n,k);
if (nv > NAUTY_INFINITY-2) gt_abort(">E genspecialg: too big -J\n");
deg = k*(n-k);
SG_ALLOC(*sg,nv,nv*(size_t)deg,"genspecialg");
sg->nv = nv;
sg->nde = nv*(size_t)deg;
SG_VDE(sg,v,d,e);
if ((a = malloc(k*sizeof(int))) == NULL ||
(b = malloc(k*sizeof(int))) == NULL)
gt_abort(">E malloc failed in makeJohnson()\n");
preparemarks(n);
for (i = 0; i < nv; ++i)
{
v[i] = i*(size_t)deg;
d[i] = deg;
ep = e + v[i];
unrank(i,k,a);
RESETMARKS;
for (j = 0; j < k; ++j) MARK(a[j]);
for (j = 0; j < n; ++j)
if (ISNOTMARKED(j))
{
for (s = 0; s < k; ++s)
{
for (t = 0; t < k; ++t) b[t] = a[t];
u = s;
while (u > 0 && b[u-1] > j)
{
b[u] = b[u-1];
--u;
}
while (u < k-1 && b[u+1] < j)
{
b[u] = b[u+1];
++u;
}
b[u] = j;
*(ep++) = rank(k,b);
}
}
}
FREES(a);
FREES(b);
}
static setword*
subsetlist(long n, long k)
/* Allocate binomial(n,k) setwords filled with right-adjusted subsets.
It is known that binomial(n,k) is small enough for an int. */
{
setword *x,w,first,last;
int i,nv;
nv = binomial(n,k);
if ((x = malloc(sizeof(setword)*nv)) == NULL)
gt_abort(">E malloc() failed in subsetlist()\n");
first = ((setword)1 << k) - 1;
last = first << (n-k);
if (k == 0 || k == n)
{
x[0] = first;
return x;
}
w = ((setword)1 << k) - 1;
last = w << (n-k);
i = 0;
for (;;)
{
if (POPCOUNT(w) == k)
{
x[i++] = w;
w += SWHIBIT(w);
if (w == last) break;
}
else
{
++w;
}
}
x[i] = last;
if (i != nv-1) gt_abort(">E something (1) wrong in subsetlist()\n");
return x;
}
/**************************************************************************/
static void
makeKneser(long n, long k, long t, boolean digraph, sparsegraph *sg)
/* Make generalized Kneser graphs. The vertices are the k-subsets of
an n-set and two are adjacent if there intersection is exactly t. */
{
size_t *v;
int *d,*e,nv,deg,i,j;
setword *x;
if (k < 0 || t < 0 || t >= k || 2*k-t > n)
gt_abort(">E genspecialg: impossible parameters for -K\n");
if (n > WORDSIZE)
gt_abort(">E genspecialg: first parameter of -K is too big\n");
if (t == k-1)
{
makeJohnson(n,k,digraph,sg);
return;
}
nv = binomial(n,k);
if (nv > NAUTY_INFINITY-2) gt_abort(">E genspecialg: too big -K\n");
deg = binomial(k,t)*binomial(n-k,k-t);
SG_ALLOC(*sg,nv,nv*(size_t)deg,"genspecialg");
sg->nv = nv;
sg->nde = nv*(size_t)deg;
SG_VDE(sg,v,d,e);
x = subsetlist(n,k);
for (i = 0; i < nv; ++i)
{
v[i] = i*(size_t)deg;
d[i] = 0;
}
for (i = 0; i < nv-1; ++i)
for (j = i+1; j < nv; ++j)
{
if (POPCOUNT(x[i]&x[j]) == t)
{
e[v[i]+(d[i]++)] = j;
e[v[j]+(d[j]++)] = i;
}
}
if (d[0] != deg) gt_abort(">E something (2) wrong in makeKneser()\n");
FREES(x);
}
/**************************************************************************/
static void
makeantiregular(long n, boolean digraph, graph **pg)
/* Make a connected antiregular graph on n vertices. The other
antiregular graph is the complement of this one and is disconnected.
The defining property is having n-1 different degrees. */
{
int i,j,m;
graph *g;
int *deg;
boolean q;
if (n < 2 || n > NAUTY_INFINITY-2)
gt_abort(">E genspecialg: bad argument for -A\n");
m = SETWORDSNEEDED(n);
if ((g = malloc(m*sizeof(graph)*n)) == NULL
|| (deg = malloc(sizeof(int)*n)) == NULL)
gt_abort(">E allocation failed in makecomplete()\n");
*pg = g;
EMPTYSET(g,m*n);
for (i = 0; i < n; ++i) deg[i] = 0;
ADDONEEDGE(g,0,1,m);
deg[0] = deg[1] = 1;
for (j = 2; j < n; ++j)
{
q = FALSE;
for (i = 0; i < j; ++i)
{
if (deg[i] > j/2)
{
ADDONEEDGE(g,i,j,m);
++deg[i];
++deg[j];
}
else if (deg[i] == j/2 && !q)
{
ADDONEEDGE(g,i,j,m);
++deg[i];
++deg[j];
q = TRUE;
}
}
}
FREES(deg);
}
/**************************************************************************/
static void
makecomplete(long n, boolean digraph, graph **pg)
{
int i,j,m;
graph *g,*gj;
if (n < 1 || n > NAUTY_INFINITY-2)
gt_abort(">E genspecialg: bad argument for -k\n");
m = SETWORDSNEEDED(n);
if ((g = malloc(m*sizeof(graph)*n)) == NULL)
gt_abort(">E allocation failed in makecomplete()\n");
*pg = g;
g[m-1] = 0;
for (i = 0; i < n; ++i) ADDELEMENT(g,i);
for (j = 1, gj = g+m; j < n; ++j, gj += m)
for (i = 0; i < m; ++i) gj[i] = g[i];
if (!digraph)
{
for (j = 0, gj = g; j < n; ++j, gj += m) DELELEMENT(gj,j);
}
}
/**************************************************************************/
static void
makemultipartite(long *args, int nargs, long *size, graph **pg)
{
graph *g,*gj,*gk;
long ln;
int i,j,k,kk,t,m,n;
ln = 0;
for (t = 0; t < nargs; ++t)
{
if (args[t] <= 0) gt_abort(">E bad part size for -m\n");
ln += args[t];
}
*size = ln;
if (ln < 1 || ln > NAUTY_INFINITY-2)
gt_abort(">E genspecialg: bad argument for -m\n");
n = ln;
m = SETWORDSNEEDED(n);
if ((g = malloc(m*sizeof(graph)*n)) == NULL)
gt_abort(">E allocation failed in makemultipartite()\n");
*pg = g;
for (t = k = 0; t < nargs; ++t, k = kk)
{
gk = g + k*m;
kk = k + args[t];
gk[m-1] = 0;
for (i = 0; i < n; ++i) ADDELEMENT(gk,i);
for (i = k; i < kk; ++i) DELELEMENT(gk,i);
for (j = k+1, gj = gk+m; j < kk; ++j, gj += m)
for (i = 0; i < m; ++i) gj[i] = gk[i];
}
}
/**************************************************************************/
static void
makeempty(long n, boolean digraph, sparsegraph *sg)
{
int *d,*e,i;
size_t *v;
if (n < 1 || n > NAUTY_INFINITY-2)
gt_abort(">E genspecialg: bad argument for -e\n");
if (digraph) SG_ALLOC(*sg,n,n,"genspecialg");
else SG_ALLOC(*sg,n,0,"genspecialg");
SG_VDE(sg,v,d,e);
if (digraph)
{
sg->nv = n;
sg->nde = n;
for (i = 0; i < n; ++i)
{
d[i] = 1;
v[i] = i;
e[i] = i;
}
}
else
{
sg->nv = n;
sg->nde = 0;
for (i = 0; i < n; ++i)
{
d[i] = 0;
v[i] = 0;
}
}
}
/**************************************************************************/
static void
makehypercube(long n, long t, boolean digraph, sparsegraph *sg)
/* Make a graph whose vertices are {0,1}^n and whose edges are
vertices at hamming distance t. */
{