On the nonexistence of graphs of diameter 2 and defect 2
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F09%3A00503074" target="_blank" >RIV/49777513:23520/09:00503074 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
On the nonexistence of graphs of diameter 2 and defect 2
Original language description
In 1960, Homan and Singleton investigated the existence of Moore graphs of diameter 2 (graphs of maximum degree d and d^2+1 vertices), and found that such graphs exist only for d = 2; 3; 7 and possibly 57. In 1980, Erdos et al., using eigenvalue analysis, showed that, with the exception of C_4, there are no graphs of diameter 2, maximum degree d and d^2 vertices. In this paper, we show that graphs of diameter 2, maximum degree d and d^2-1 vertices do not exist for most values of d with d at least 6, andconjecture that they do not exist for any d greater or equal to 6.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
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Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2009
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Combinatorial Mathematics and Combinatorial Computing
ISSN
0835-3026
e-ISSN
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Volume of the periodical
71
Issue of the periodical within the volume
1
Country of publishing house
CA - CANADA
Number of pages
16
Pages from-to
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UT code for WoS article
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EID of the result in the Scopus database
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