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Naslov:On bipartite Q-polynominal distance-regular graphs
Avtorji:ID Miklavič, Štefko (Avtor)
Datoteke:URL http://dx.doi.org/10.1016/j.ejc.2005.09.003
 
Jezik:Angleški jezik
Vrsta gradiva:Delo ni kategorizirano
Tipologija:1.01 - Izvirni znanstveni članek
Organizacija:IAM - Inštitut Andrej Marušič
Opis:Let Γ denote a bipartite Q-polynomial distance-regular graph with vertex set X, diameter d3 and valency k3. Let RX denote the vector space over R consisting of column vectors with entries in r and rows indexed by X. For zX, let ˆz denote the vector in RX with a 1 in the z-coordinate, and 0 in all other coordinates. Fix x,yX such that (x,y)=2,where$ denotes the path-length distance. For 0i,jd define wij=ˆz, where the sum is over all zX such that (x,z)=i and (y,z)=j$.Wedefine$W=span{wij|0i,jd}. In this paper we consider the space MW=span{mw|mM,wW\l}, where M is the Bose-Mesner algebra of Γ. We observe that MW is the minimal A-invariant subspace of RX which contains W, where A is the adjacency matrix of Γ. We display a basis for MW that is orthogonal with respect to the dot product. We give the action of A on this basis. We show that the dimension of MW is 3d3 if Γ is 2-homogeneous, 3d1 if Γ is the antipodal quotient of the 2d-cube, and 4d4 otherwise. We obtain our main result using Terwilliger's "balanced set" characterization of the Q-polynomial property.
Ključne besede:mathematics, graph theory, distance-regular graphs, Q-polynominal property, Bose-Mesner algebra, balanced set characterization of the Q-polynominal property
Leto izida:2007
Št. strani:str. 94-110
Številčenje:Vol. 28, no. 1
PID:20.500.12556/RUP-3312 Povezava se odpre v novem oknu
ISSN:0195-6698
UDK:519.17
COBISS.SI-ID:1796823 Povezava se odpre v novem oknu
Datum objave v RUP:15.10.2013
Število ogledov:5028
Število prenosov:29
Metapodatki:XML DC-XML DC-RDF
:
MIKLAVIČ, Štefko, 2007, On bipartite Q-polynominal distance-regular graphs. [na spletu]. 2007. Vol. 28, no. 1, p. 94–110. [Dostopano 19 marec 2025]. Pridobljeno s: http://dx.doi.org/10.1016/j.ejc.2005.09.003
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Sekundarni jezik

Jezik:Angleški jezik
Ključne besede:matematika, teorija grafov, razdaljno regularni grafi, Q-polinomska lastnost, Bose-Mesnerjeva algebra


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