On bipartite ▫$Q$▫-polynomial distance-regular graphs with ▫$c_2=1$▫
Miklavič, Štefko
Naj bo ▫$\Gamma$▫ dvodelen ▫$Q$▫-polinomski razdaljno regularen graf premera ▫$d \ge 3$▫, stopnje ▫$k \ge 3$▫ in presečnim številom ▫$c_2=1$▫. Pokažemo, da množica vozlišč grafa ▫$\Gamma$▫ premore ...ekvitabilno particijo, ki vsebuje ▫$4d-4$▫ množic. S pomočjo te ekvitabilne particije doka\emo, da morajo presečna števila grafa ▫$\Gamma$▫ zadoščati naslednjim pogojem: (I) ▫$c_{i+1}-1$▫ deli ▫$c_i(c_i-1)$▫ za ▫$2 \le i \le d-1$▫, (II) ▫$b_{i-1}-1$▫ deli ▫$b_i(b_i-1)$▫ za ▫$1 \le i \le d-1$▫. S pomočjo teh pogojev dokažemo, da graf ▫$\Gamma$▫ ne obstaja, če je ▫$d=4$▫.
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