Geodesic
Shilla graphs with $b = 5$ and $b = 6$
Ural mathematical journal, Tome 7 (2021) no. 2, pp. 51-58

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A $Q$-polynomial Shilla graph with ${b = 5}$ has intersection arrays ${\{105t,4(21t+1),16(t+1);}$ ${1,4 (t+1),84t\}}$, $t\in\{3,4,19\}$. The paper proves that distance-regular graphs with these intersection arrays do not exist. Moreover, feasible intersection arrays of $Q$-polynomial Shilla graphs with $b = 6$ are found.
Keywords: Shilla graph, distance-regular graph
Mots-clés : $Q$-polynomial graph. 
@article{UMJ_2021_7_2_a3,
     author = {Alexander A. Makhnev and Ivan N. Belousov},
     title = {Shilla graphs with $b = 5$ and $b = 6$},
     journal = {Ural mathematical journal},
     pages = {51--58},
     publisher = {mathdoc},
     volume = {7},
     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UMJ_2021_7_2_a3/}
}
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Alexander A. Makhnev; Ivan N. Belousov. Shilla graphs with $b = 5$ and $b = 6$. Ural mathematical journal, Tome 7 (2021) no. 2, pp. 51-58. http://geodesic.mathdoc.fr/item/UMJ_2021_7_2_a3/