Geodesic
On bipartite \(Q\)-polynomial distance-regular graphs with diameter 9, 10, or 11
Štefko Miklavič1
1University of Primorska
The electronic journal of combinatorics, Tome 25 (2018) no. 1
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Let $\Gamma$ denote a bipartite distance-regular graph with diameter $D$. In [Caughman (2004)], Caughman showed that if $D \ge 12$, then $\Gamma$ is $Q$-polynomial if and only if one of the following (i)-(iv) holds: (i) $\Gamma$ is the ordinary $2D$-cycle, (ii) $\Gamma$ is the Hamming cube $H(D,2)$, (iii) $\Gamma$ is the antipodal quotient of the Hamming cube $H(2D,2)$, (iv) the intersection numbers of $\Gamma$ satisfy $c_i = (q^i - 1)/(q-1)$, $b_i = (q^D-q^i)/(q-1)$ $(0 \le i \le D)$, where $q$ is an integer at least $2$. In this paper we show that the above result is true also for bipartite distance-regular graphs with $D \in \{9,10,11\}$.
DOI : 10.37236/7347
Classification : 05C50, 05E30
Mots-clés : bipartite distance-regular graphs, \(Q\)-polynomial property

Štefko Miklavič  1

1 University of Primorska 
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     author = {\v{S}tefko Miklavi\v{c}},
     title = {On bipartite {\(Q\)-polynomial} distance-regular graphs with diameter 9, 10, or 11},
     journal = {The electronic journal of combinatorics},
     year = {2018},
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     number = {1},
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Štefko Miklavič. On bipartite \(Q\)-polynomial distance-regular graphs with diameter 9, 10, or 11. The electronic journal of combinatorics, Tome 25 (2018) no. 1. doi: 10.37236/7347

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