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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

  • DOI - Digital Object Identifier

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

  • Czech description

Classification

  • Type

    J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

Result continuities

  • Project

  • 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

  • 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

  • UT code for WoS article

  • EID of the result in the Scopus database