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Mat. Zametki, 2003, Volume 74, Issue 3, Pages 396–406 (Mi mz273)  

This article is cited in 9 scientific papers (total in 10 papers)

On Crown-Free Graphs with Regular $\mu$-Subgraphs, II

V. V. Kabanov, A. A. Makhnev, D. V. Paduchikh

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: The crown is the complete multipartite graph $K_{1,1,3}$. Terwilliger graphs without crowns and graphs without 3-cocliques with regular $\mu$-subgraphs of given positive degree are studied. As a corollary, the local structure of graphs in which the neighborhoods of vertices are regular Terwilliger graphs of diameter 2 and some of these neighborhoods contain no 7-paws is determined. Connected crown-free graphs in which $\mu$-subgraphs are edge regular graphs of diameter not exceeding 2 with given parameters are described.

DOI: https://doi.org/10.4213/mzm273

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English version:
Mathematical Notes, 2003, 74:3, 375–384

Bibliographic databases:

UDC: 519.14
Received: 25.03.2002

Citation: V. V. Kabanov, A. A. Makhnev, D. V. Paduchikh, “On Crown-Free Graphs with Regular $\mu$-Subgraphs, II”, Mat. Zametki, 74:3 (2003), 396–406; Math. Notes, 74:3 (2003), 375–384

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. A. L. Gavrilyuk, A. A. Makhnev, “Terwilliger Graphs with $\mu\le3$”, Math. Notes, 82:1 (2007), 13–24  mathnet  crossref  crossref  mathscinet  isi  elib
    2. V. V. Kabanov, S. V. Unegov, “Strongly regular graphs with Hoffman's condition”, Proc. Steklov Inst. Math. (Suppl.), 261, suppl. 1 (2008), S107–S112  mathnet  crossref  elib
    3. Zyulyarkina, ND, “Graphs in which the neighborhoods of all vertices are clique extensions of grids”, Doklady Mathematics, 76:2 (2007), 758  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    4. Kabanov, VV, “Characterization of certain distance-regular graphs by forbidden subgraphs”, Doklady Mathematics, 75:3 (2007), 420  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    5. V. V. Kabanov, S. V. Unegov, “Amply regular graphs with Hoffman's condition”, Proc. Steklov Inst. Math. (Suppl.), 264, suppl. 1 (2009), S150–S154  mathnet  crossref  isi  elib
    6. V. V. Kabanov, A. A. Makhnev, D. V. Paduchikh, “Grafy bez 3-koron s nekotorymi usloviyami regulyarnosti”, Tr. IMM UrO RAN, 14, no. 4, 2008, 53–69  mathnet  elib
    7. G. M. Ermakova, V. V. Kabanov, “A characterization of one class of graphs without 3-claws”, Proc. Steklov Inst. Math. (Suppl.), 267, suppl. 1 (2009), S62–S77  mathnet  crossref  isi  elib
    8. Kabanov V., “Graphs and Transitive Permutation Groups”: Simos, TE, Numerical Analysis and Applied Mathematics, Vols I-III, AIP Conference Proceedings, 1281, ed. Psihoyios G. Tsitouras C., Amer Inst Physics, 2010, 908–910  mathscinet  adsnasa  isi
    9. Gavrilyuk A.L., Makhnev A.A., “On graphs in which the intersection of neighborhoods of vertices from every 3-coclique is a clique”, Doklady Mathematics, 83:1 (2011), 1–4  crossref  mathscinet  zmath  isi  elib  elib  scopus
    10. “Makhnev Aleksandr Alekseevich (on his 60th birthday)”, Proc. Steklov Inst. Math. (Suppl.), 285, suppl. 1 (2014), 1–11  mathnet  crossref  mathscinet
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