how can i construct a strongly regular graph with parameter $(275,112,30,56)$(Mclaughlin Graph), (105,32,4,12)?


I need adjacency matrix of them?


I know they are unique.



Mclaughlin Graph
You can construct the McLaughlin graph using [GAP](http://www.gap-system.org/).



```
gap> LoadPackage("AtlasRep");;  
gap> mcl:=Group(AtlasGenerators("McL",1).generators);;
gap> LoadPackage("grape");;
gap> Gr:=NullGraph(mcl);;
gap> AddEdgeOrbit(Gr,[1,2]);;
gap> VertexDegrees(Gr);
[ 112 ]

```

OK, so that's the 1st graph. For the 2nd graph, one has to take various subgraphs and complements of the 1st one:



```
gap> GrC:=ComplementGraph(Gr);; 
gap> GrC1:=InducedSubgraph(GrC,Adjacency(GrC,1));;
gap> VertexDegrees(GrC1);
[ 105 ]
gap> GrC12:=InducedSubgraph(GrC1,Adjacency(GrC1,1));;
gap> VertexDegrees(GrC12);                           
[ 72 ]
gap> G2:=ComplementGraph(GrC12);;                    
gap> VertexDegrees(GrC12);       
[ 72 ]
gap> VertexDegrees(G2);   
[ 32 ]
gap> GlobalParameters(G2); #indeed, that's the graph you asked for:
[ [ 0, 0, 32 ], [ 1, 4, 27 ], [ 12, 20, 0 ] ]

```

Printing the adjacency matrices of graphs in GAP is easy too, using `IsEdge` function. (But do you really need it? You can work with these graphs directly in `GAP`, without much extra trouble.)


