Diskretnaya Matematika
 RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Diskr. Mat.: Year: Volume: Issue: Page: Find

 Diskr. Mat., 2020, Volume 32, Issue 1, Pages 74–80 (Mi dm1595)

On a distance-regular graphs with $c_2=2$

A. A. Makhnevab, M. S. Nirovaab

a Institute of Mathematics and Mechanics UB RAS
b Kabardino-Balkarskii State University

Abstract: Let $\Gamma$ be a distance-regular graph of diameter $d=3$ with $c_2=2$. Then local subgraph $\Delta$ of the vertex $w$ of $\Gamma$ is a partial line spase. By some Brouwer-Neumaier result either $\Delta$ is the union of $(a_1+1)$-cliques or $k\ge a_1(a_1+3)/2$, and in the case equality we have $k=5, \lambda=2$ and $\Gamma$ is icosahedron.
A.A. Makhnev, M.P. Golubyatnikov and Wenbin Guo investigate distance-regular graphs $\Gamma$ with $\Gamma_3$ being pseudo-geometric graph for net. They found a new infinite series $\{2u^2-2m^2+4m-3,2u^2-2m^2,u^2-m^2+4m-2;1,2,u^2-m^2\}$ feasible intersection arrays for such graphs with $c_2=2$. In the paper it is proved that some graphs with arrays from this series do not exist. Also it is proved that distance-regular graph with intersection array $\{22,16,5;1,2,20\}$ does not exist.

Keywords: distance-regular graph, partial line space, graph with $c_2=2$.

 Funding Agency Grant Number Ural Branch of the Russian Academy of Sciences 18-1-1-17 Ministry of Education and Science of the Russian Federation 02.A03.21.0006

DOI: https://doi.org/10.4213/dm1595

Full text: PDF file (435 kB)
First page: PDF file
References: PDF file   HTML file

Bibliographic databases:

UDC: 519.172

Citation: A. A. Makhnev, M. S. Nirova, “On a distance-regular graphs with $c_2=2$”, Diskr. Mat., 32:1 (2020), 74–80

Citation in format AMSBIB
\Bibitem{MakNir20} \by A.~A.~Makhnev, M.~S.~Nirova \paper On a distance-regular graphs with $c_2=2$ \jour Diskr. Mat. \yr 2020 \vol 32 \issue 1 \pages 74--80 \mathnet{http://mi.mathnet.ru/dm1595} \crossref{https://doi.org/10.4213/dm1595} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=4075903}