Geodesic
Using symbolic computation to prove nonexistence of distance-regular graphs
Janoš Vidali1
1University of Ljubljana, Faculty of Mathematics and Physics
The electronic journal of combinatorics, Tome 25 (2018) no. 4
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A package for the Sage computer algebra system is developed for checking feasibility of a given intersection array for a distance-regular graph. We use this tool to show that there is no distance-regular graph with intersection array$$\{(2r+1)(4r+1)(4t-1), 8r(4rt-r+2t), (r+t)(4r+1); 1, (r+t)(4r+1), 4r(2r+1)(4t-1)\} (r, t \geq 1),$$$\{135,\! 128,\! 16; 1,\! 16,\! 120\}$, $\{234,\! 165,\! 12; 1,\! 30,\! 198\}$ or $\{55,\! 54,\! 50,\! 35,\! 10; 1,\! 5,\! 20,\! 45,\! 55\}$. In all cases, the proofs rely on equality in the Krein condition, from which triple intersection numbers are determined. Further combinatorial arguments are then used to derive nonexistence.
DOI : 10.37236/7763
Classification : 05E30
Mots-clés : distance-regular graphs, Krein parameters, triple intersection numbers, nonexistence, symbolic computation

Janoš Vidali  1

1 University of Ljubljana, Faculty of Mathematics and Physics 
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     title = {Using symbolic computation to prove nonexistence of distance-regular graphs},
     journal = {The electronic journal of combinatorics},
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Janoš Vidali. Using symbolic computation to prove nonexistence of distance-regular graphs. The electronic journal of combinatorics, Tome 25 (2018) no. 4. doi: 10.37236/7763

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