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On Distance-Regular Graphs of Diameter 3 With Eigenvalue 0. / Makhnev, A. A.; Belousov, I. N.
In: Siberian Advances in Mathematics, Vol. 33, No. 1, 2023, p. 56-65.

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Harvard

Makhnev, AA & Belousov, IN 2023, 'On Distance-Regular Graphs of Diameter 3 With Eigenvalue 0', Siberian Advances in Mathematics, vol. 33, no. 1, pp. 56-65. https://doi.org/10.1134/S1055134423010054

APA

Makhnev, A. A., & Belousov, I. N. (2023). On Distance-Regular Graphs of Diameter 3 With Eigenvalue 0. Siberian Advances in Mathematics, 33(1), 56-65. https://doi.org/10.1134/S1055134423010054

Vancouver

Makhnev AA, Belousov IN. On Distance-Regular Graphs of Diameter 3 With Eigenvalue 0. Siberian Advances in Mathematics. 2023;33(1):56-65. doi: 10.1134/S1055134423010054

Author

Makhnev, A. A. ; Belousov, I. N. / On Distance-Regular Graphs of Diameter 3 With Eigenvalue 0. In: Siberian Advances in Mathematics. 2023 ; Vol. 33, No. 1. pp. 56-65.

BibTeX

@article{a7be0b6e7af44d83bcee9bf5cc264eea,
title = "On Distance-Regular Graphs of Diameter 3 With Eigenvalue 0",
abstract = "For a distance-regular graph (Formula presented.) of diameter 3, the graph (Formula presented.) can be strongly regular only if either i=2 or i=3. For the case inwhich (Formula presented.) is strongly regular, Koolen and his coauthors foundparameters of (Formula presented.) in terms of the intersection array of (Formula presented.) (these parameters were obtained independently byMakhnev and Paduchikh). In this case, one of the eigenvalues of (Formula presented.) is (Formula presented.). In the present article, we consider graphs with eigenvalues (Formula presented.) and (Formula presented.). We prove that the intersection array of (Formula presented.) is (Formula presented.). For (Formula presented.), we show that the intersection array of (Formula presented.) is either (Formula presented.), or (Formula presented.), or (Formula presented.), or (Formula presented.). {\textcopyright} 2023, Pleiades Publishing, Ltd.",
author = "Makhnev, {A. A.} and Belousov, {I. N.}",
year = "2023",
doi = "10.1134/S1055134423010054",
language = "English",
volume = "33",
pages = "56--65",
journal = "Siberian Advances in Mathematics",
issn = "1055-1344",
publisher = "Springer Verlag",
number = "1",

}

RIS

TY - JOUR

T1 - On Distance-Regular Graphs of Diameter 3 With Eigenvalue 0

AU - Makhnev, A. A.

AU - Belousov, I. N.

PY - 2023

Y1 - 2023

N2 - For a distance-regular graph (Formula presented.) of diameter 3, the graph (Formula presented.) can be strongly regular only if either i=2 or i=3. For the case inwhich (Formula presented.) is strongly regular, Koolen and his coauthors foundparameters of (Formula presented.) in terms of the intersection array of (Formula presented.) (these parameters were obtained independently byMakhnev and Paduchikh). In this case, one of the eigenvalues of (Formula presented.) is (Formula presented.). In the present article, we consider graphs with eigenvalues (Formula presented.) and (Formula presented.). We prove that the intersection array of (Formula presented.) is (Formula presented.). For (Formula presented.), we show that the intersection array of (Formula presented.) is either (Formula presented.), or (Formula presented.), or (Formula presented.), or (Formula presented.). © 2023, Pleiades Publishing, Ltd.

AB - For a distance-regular graph (Formula presented.) of diameter 3, the graph (Formula presented.) can be strongly regular only if either i=2 or i=3. For the case inwhich (Formula presented.) is strongly regular, Koolen and his coauthors foundparameters of (Formula presented.) in terms of the intersection array of (Formula presented.) (these parameters were obtained independently byMakhnev and Paduchikh). In this case, one of the eigenvalues of (Formula presented.) is (Formula presented.). In the present article, we consider graphs with eigenvalues (Formula presented.) and (Formula presented.). We prove that the intersection array of (Formula presented.) is (Formula presented.). For (Formula presented.), we show that the intersection array of (Formula presented.) is either (Formula presented.), or (Formula presented.), or (Formula presented.), or (Formula presented.). © 2023, Pleiades Publishing, Ltd.

UR - http://www.scopus.com/inward/record.url?partnerID=8YFLogxK&scp=85151081386

U2 - 10.1134/S1055134423010054

DO - 10.1134/S1055134423010054

M3 - Article

VL - 33

SP - 56

EP - 65

JO - Siberian Advances in Mathematics

JF - Siberian Advances in Mathematics

SN - 1055-1344

IS - 1

ER -

ID: 37143531