| Naslov: | On the uniform structure of bipartite graphs admitting a dual adjacency matrix candidate |
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| Avtorji: | ID Fernández, Blas (Avtor)
ID Maleki, Roghayeh (Avtor)
ID Miklavič, Štefko (Avtor)
ID Monzillo, Giusy (Avtor) |
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| Datoteke: |  RAZ_Fernandez_Blas_2026.pdf (318,25 KB)
MD5: 756505BF6B17A60B9FF97ED6DCB72932
 https://link.springer.com/article/10.1007/s10801-026-01546-3
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| Jezik: | Angleški jezik |
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| Vrsta gradiva: | Članek v reviji |
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| Tipologija: | 1.01 - Izvirni znanstveni članek |
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| Organizacija: | FAMNIT - Fakulteta za matematiko, naravoslovje in informacijske tehnologije
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| Opis: | Let Γ denote a finite, bipartite, connected graph with vertex set X. Fix x ∈ X and let ε ≥ 3 denote the eccentricity of x. For mutually distinct scalars {θ ∗ i }ε i=0 define a diagonal matrix A∗ = A∗(θ ∗ 0 , θ ∗ 1 , . . . , θ ∗ ε ) ∈ Mat X (R) as follows: for y ∈ X set (A∗)yy = θ ∗ ∂(x,y), where ∂ denotes the shortest path-length distance function of Γ. We say that A∗ is a dual adjacency matrix candidate of Γ with respect to x if the adjacency matrix A ∈ Mat X (R) of Γ and A∗ satisfy A3 A∗ − A∗ A3 + (β + 1)(A A∗ A2 − A2 A∗ A) = ρ(A A∗ − A∗ A) for some scalars β, ρ ∈ R. In this paper, we investigate when bipartite graphs that admit a dual adjacency matrix candidate also admit a uniform structure (in the sense of Terwilliger [6]). To do that, we first define a weakly uniform structure by slightly relaxing the conditions of uniform structure. The main result of this paper is that Γ admits a dual adjacency matrix candidate with respect to x if and only if Γ admits a weakly uniform structure with respect to x whose parameters satisfy some additional conditions. In particular, for β = 2, the weakly uniform structure is indeed a uniform structure. |
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| Ključne besede: | uniform property, dual adjacency matrix, Q-polynomial property |
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| Verzija publikacije: | Objavljena publikacija |
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| Datum objave: | 05.06.2026 |
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| Leto izida: | 2026 |
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| Št. strani: | str. 1-17 |
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| Številčenje: | Vol. 63, iss. 4, article no. 60 |
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| PID: | 20.500.12556/RUP-23157  |
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| UDK: | 519.17 |
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| ISSN pri članku: | 0925-9899 |
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| DOI: | 10.1007/s10801-026-01546-3 |
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| COBISS.SI-ID: | 282133507 |
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| Datum objave v RUP: | 18.06.2026 |
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| Število ogledov: | 26 |
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| Število prenosov: | 2 |
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| Metapodatki: |    |
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