20.500.12556/RUP-286
On bipartite Q-polynomial distance-regular graphs with c [sub] 2 [equal] 1
Let ▫$\Gamma$▫ denote a bipartite ▫$Q$▫-polynomial distance-regular graph with diameter ▫$d \ge 3$▫, valency ▫$k \ge 3$▫ and intersection number ▫$c_2=1$▫. We show that ▫$\Gamma$▫ has a certain equitable partition of its vertex set which involves ▫$4d-4$▫ cells. We use this partition to show that the intersection numbers of ▫$\Gamma$▫ satisfy the following divisibility conditions: (I) ▫$c_{i+1}-1$▫ divides ▫$c_i(c_i-1)$▫ for ▫$2 \le i \le d-1$▫, and (II) ▫$b_{i-1}-1$▫ divides ▫$b_i(b_i-1)$▫ for ▫$1 \le i \le d-1$▫. Using these divisibility conditions we show that ▫$\Gamma$▫ does not exist if ▫$d=4$▫.
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 ▫$d=4$▫.
mathematics
grah theory
distance-regular graphs
▫$Q$▫-polynomial property
equitable partitions
matematika
teorija grafov
razdaljno regularni grafi
▫$Q$▫-polinomska lastnost
ekvitabilne particije
true
true
false
Angleški jezik
Slovenski jezik
Delo ni kategorizirano
2013-10-15 12:04:40
2013-10-15 12:04:40
2024-03-01 11:55:03
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2007
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str. 544-553
iss. 3-5
Vol. 307
2007
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NiDoloceno
NiDoloceno
NiDoloceno
0000-00-00
0000-00-00
0000-00-00
0012-365X
519.17
14181465
http://dx.doi.org/10.1016/j.disc.2005.09.044
1
https://repozitorij.upr.si/Dokument.php?lang=slv&id=286
Inštitut Andrej Marušič
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