On bipartite graphs of diameter 3 and defect 2

Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F09%3A00503071" target="_blank" >RIV/49777513:23520/09:00503071 - isvavai.cz</a>
Výsledek na webu
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DOI - Digital Object Identifier
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Jazyk výsledku
angličtina
Název v původním jazyce
On bipartite graphs of diameter 3 and defect 2
Popis výsledku v původním jazyce
We consider bipartite graphs of degree d at least 2, diameter 3, and defect 2 (having 2 vertices less than the bipartite Moore bound). Such graphs are called bipartite (d,3,-2) -graphs. We prove the uniqueness of the known bipartite (3,3,-2) -graph and bipartite (4,3,-2)-graph. We also prove several necessary conditions for the existence of bipartite (d,3,-2) -graphs. The most general of these conditions is that either d or d-2 must be a perfect square. Furthermore, in some cases for which the conditionholds, in particular, when d=6 and d=9, we prove the non-existence of the corresponding bipartite (d,3,-2)-graphs.
Název v anglickém jazyce
On bipartite graphs of diameter 3 and defect 2
Popis výsledku anglicky
We consider bipartite graphs of degree d at least 2, diameter 3, and defect 2 (having 2 vertices less than the bipartite Moore bound). Such graphs are called bipartite (d,3,-2) -graphs. We prove the uniqueness of the known bipartite (3,3,-2) -graph and bipartite (4,3,-2)-graph. We also prove several necessary conditions for the existence of bipartite (d,3,-2) -graphs. The most general of these conditions is that either d or d-2 must be a perfect square. Furthermore, in some cases for which the conditionholds, in particular, when d=6 and d=9, we prove the non-existence of the corresponding bipartite (d,3,-2)-graphs.

Druh
J<sub>x</sub> - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
CEP obor
BA - Obecná matematika
OECD FORD obor
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Rok uplatnění
2009
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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