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Sbornik: Mathematics, 1996, Volume 187, Issue 10, Pages 1487–1501
DOI: https://doi.org/10.1070/SM1996v187n10ABEH000165 (Mi sm165) 		 
This article is cited in 9 scientific papers (total in 10 papers)

On separated graphs with certain regularity conditions

V. V. Kabanova, A. A. Makhnevb

a Ural State Technical University
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
English version PDF (730 kB) Citations (10)
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DOI: https://doi.org/10.1070/SM1996v187n10ABEH000165
Abstract: Two theorems are proved in this paper. Theorem I describes the connected $\mu$-regular graphs without 3-claws. Necessary and sufficient conditions for a connected amply regular graph with $\mu >1$ to be separated are obtained in Theorem 2. A graph $\Gamma$ is said to be separated if for any vertex $a$ in $\Gamma$ the subgraph $\Gamma _2(a)$ contains vertices $b$ and $c$ at a distance 2 in $\Gamma _2(a)$, and the $\mu$-subgraph for any such pair does not intersect the neighbourhood of $a$.
Received: 10.10.1994 and 20.09.1995
Russian version:
Matematicheskii Sbornik, 1996, Volume 187, Number 10, Pages 73–86
DOI: https://doi.org/10.4213/sm165
Bibliographic databases:
UDC: 519.17
MSC: Primary 05C75; Secondary 05C12, 05E30
Language: English
Original paper language: Russian
Citation: V. V. Kabanov, A. A. Makhnev, “On separated graphs with certain regularity conditions”, Mat. Sb., 187:10 (1996), 73–86; Sb. Math., 187:10 (1996), 1487–1501
Citation in format AMSBIB
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\by V.~V.~Kabanov, A.~A.~Makhnev
\paper On separated graphs with certain regularity conditions
\jour Mat. Sb.
\yr 1996
\vol 187
\issue 10
\pages 73--86
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\transl
\jour Sb. Math.
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\pages 1487--1501
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:418
    Russian version PDF:165
    English version PDF:10
    References:41
    First page:1
     
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