Quelle gpolygons_incgraph.include
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gap> blocks := [
> [ 1, 2, 3, 4, 5 ], [ 1, 6, 7, 8, 9 ], [ 1, 10, 11, 12, 13 ],
> [ 1, 14, 15, 16, 17 ], [ 1, 18, 19, 20, 21 ], [ 2, 6, 10, 14, 18 ],
> [ 2, 7, 11, 15, 19 ], [ 2, 8, 12, 16, 20 ], [ 2, 9, 13, 17, 21 ],
> [ 3, 6, 11, 16, 21 ], [ 3, 7, 10, 17, 20 ], [ 3, 8, 13, 14, 19 ],
> [ 3, 9, 12, 15, 18 ], [ 4, 6, 12, 17, 19 ], [ 4, 7, 13, 16, 18 ],
> [ 4, 8, 10, 15, 21 ], [ 4, 9, 11, 14, 20 ], [ 5, 6, 13, 15, 20 ],
> [ 5, 7, 12, 14, 21 ], [ 5, 8, 11, 17, 18 ], [ 5, 9, 10, 16, 19 ] ];;
gap> gp := GeneralisedPolygonByBlocks( blocks );
<projective plane order 4>
gap> incgraph := IncidenceGraph( gp );;
gap> Diameter( incgraph );
3
gap> Girth( incgraph );
6
gap> VertexDegrees( incgraph );
[ 5 ]
gap> aut := AutGroupGraph( incgraph );
<permutation group with 9 generators>
gap> DisplayCompositionSeries(aut);
G (9 gens, size 241920)
| Z(2)
S (5 gens, size 120960)
| Z(2)
S (5 gens, size 60480)
| Z(3)
S (4 gens, size 20160)
| A(2,4) = L(3,4)
1 (0 gens, size 1)
gap> gp := ParabolicQuadric(4,4);
Q(4, 4)
gap> incgraph := IncidenceGraph( gp );;
Error, No collineation group computed. Please compute collineation group before compu
ting incidence graph,n called from
<function "unknown">( <arguments> )
called from read-eval loop at line 24 of *stdin*
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
brk> quit;
gap> CollineationGroup(gp);
PGammaO(5,4)
gap> Order(last);
1958400
gap> incgraph := IncidenceGraph( gp );;
#I Computing incidence graph of generalised polygon...
gap> aut := AutGroupGraph( incgraph );
<permutation group with 10 generators>
gap> Order(aut);
3916800
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2026-03-28
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