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This code generated zero - divisor graphs for . Enter a value for and hit <Enter> from the number keypad, or <Shift-Enter> from your laptop.
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p
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p=15;vertexlist={};For[i=1,i<p,i++,For[j=1,j≤i,j++,If[Mod[ij,p]==0,AppendTo[vertexlist,ij]]];];GraphPlot[vertexlist,VertexLabelsAutomatic]
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p=10;vertexlist={};For[i=1,i<p,i++,For[j=1,j≤i,j++,If[Mod[ij,p]==0,AppendTo[vertexlist,ij]]];];GraphPlot[vertexlist,VertexLabelsAutomatic,GraphLayout"MultipartiteEmbedding"]
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p=4*23;vertexlist={};For[i=1,i<p,i++,For[j=1,j<=i,j++,If[Mod[ij,p]==0,AppendTo[vertexlist,i->j]]];];GraphPlot[vertexlist,VertexLabels->Automatic,GraphLayout->"CircularEmbedding"]
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This graph is not bipartite. What happens if you try to graph it as bipartite?
p=4*23;vertexlist={};For[i=1,i<p,i++,For[j=1,j≤i,j++,If[Mod[ij,p]==0,AppendTo[vertexlist,ij]]];];GraphPlot[vertexlist,VertexLabelsAutomatic,GraphLayout"BipartiteEmbedding"]
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GraphPlot[{234,238,2312,2316,2320,2423,2823,3223,3623,4023,4423,462,464,466,468,4610,4612,4614,4616,4618,4620,4622,4624,4626,4628,4630,4632,4634,4636,4638,4640,4642,4644,4646,4823,4846,5046,5223,5246,5446,5623,5646,5846,6023,6046,6246,6423,6446,6646,6823,6846,694,698,6912,6916,6920,6924,6928,6932,6936,6940,6944,6948,6952,6956,6960,6964,6968,7046,7223,7246,7269,7446,7623,7646,7669,7846,8023,8046,8069,8246,8423,8446,8469,8646,8823,8846,8869,9046},VertexLabelsAutomatic,GraphLayoutBipartiteEmbedding]