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The strongly regular (40, 12, 2, 4) graphs
The electronic journal of combinatorics, Tome 7 (2000)
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In a previous paper it was established that there are at least $27$ non-isomorphic strongly regular $(40,12,2,4)$ graphs. Using a different and more efficient method we have re-investigated these graphs and have now been able to determine them all, and so complete the classification. We have discovered that there are precisely $28$ non-isomorphic $(40,12,2,4)$ strongly regular graphs. The one that was not found in the previous investigation is characterised uniquely by the fact that every neighbour graph is triangle-free.
DOI : 10.37236/1500
Classification : 05E30
Mots-clés : classification, strongly regular graphs 
@article{10_37236_1500,
     author = {E. Spence},
     title = {The strongly regular (40, 12, 2, 4) graphs},
     journal = {The electronic journal of combinatorics},
     year = {2000},
     volume = {7},
     doi = {10.37236/1500},
     zbl = {0940.05072},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1500/}
}
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E. Spence. The strongly regular (40, 12, 2, 4) graphs. The electronic journal of combinatorics, Tome 7 (2000). doi: 10.37236/1500

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