Geodesic
Nonexistence of a class of distance-regular graphs
The electronic journal of combinatorics, Tome 22 (2015) no. 2
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Let $\Gamma$ denote a distance-regular graph with diameter $D \geq 3$ and intersection numbers $a_1=0, a_2 \neq 0$, and $c_2=1$. We show a connection between the $d$-bounded property and the nonexistence of parallelograms of any length up to $d+1$. Assume further that $\Gamma$ is with classical parameters $(D, b, \alpha, \beta)$, Pan and Weng (2009) showed that $(b, \alpha, \beta)= (-2, -2, ((-2)^{D+1}-1)/3).$ Under the assumption $D \geq 4$, we exclude this class of graphs by an application of the above connection.
DOI : 10.37236/3356
Classification : 05C12, 05E30
Mots-clés : distance-regular graph, classical parameters, parallelogram, strongly closed subgraph, \(D\)-bounded 
@article{10_37236_3356,
     author = {Yu-pei Huang and Yeh-jong Pan and Chih-wen Weng},
     title = {Nonexistence of a class of distance-regular graphs},
     journal = {The electronic journal of combinatorics},
     year = {2015},
     volume = {22},
     number = {2},
     doi = {10.37236/3356},
     zbl = {1325.05066},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/3356/}
}
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Yu-pei Huang; Yeh-jong Pan; Chih-wen Weng. Nonexistence of a class of distance-regular graphs. The electronic journal of combinatorics, Tome 22 (2015) no. 2. doi: 10.37236/3356

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