Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports]
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Sib. Èlektron. Mat. Izv.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2016, Volume 13, Pages 375–387
DOI: https://doi.org/10.17377/semi.2016.13.033
(Mi semr682)
 

This article is cited in 5 scientific papers (total in 5 papers)

Discrete mathematics and mathematical cybernetics

Structure of the diversity vector of balls of a typical graph with given diameter

T. I. Fedoryaeva

Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
Full-text PDF (217 kB) Citations (5)
References:
Abstract: For labeled $n$-vertex graphs with fixed diameter $d\geq 1$, the diversity vectors of balls (the ith component of the vector is equal to the number of different balls of radius $i$) are studied asymptotically. An explicit description of the diversity vector of balls of a typical graph with given diameter is obtained. A set of integer vectors $\Lambda_{n,d}$ consisting of $\lfloor\frac{d-1}{2}\rfloor$ different vectors for $d\geq 5$ and a unique vector for $d<5$ is found. It is proved that almost all labeled $n$-vertex graphs of diameter $d$ have the diversity vector of balls belonging to $\Lambda_ {n,d}$. It is established that this property is not valid after removing any vector from $\Lambda_ {n,d}$. A number of properties of a typical graph of diameter $d$ is proved. In particular, it is obtained that such a graph for $d\geq 3$ does not possess the local $2$-diversity of balls and at the same time has the local $1$-diversity of balls, but has the full diversity of balls if $d=1,2$.
Keywords: graph, labeled graph, distance, metric ball, number of balls, diversity vector of balls, typical graph.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00507_а
Received May 5, 2016, published May 18, 2016
Document Type: Article
UDC: 519.1+519.173
MSC: 05C12
Language: Russian
Citation: T. I. Fedoryaeva, “Structure of the diversity vector of balls of a typical graph with given diameter”, Sib. Èlektron. Mat. Izv., 13 (2016), 375–387
Citation in format AMSBIB
\Bibitem{Fed16}
\by T.~I.~Fedoryaeva
\paper Structure of the diversity vector of balls of a typical graph with given diameter
\jour Sib. \`Elektron. Mat. Izv.
\yr 2016
\vol 13
\pages 375--387
\mathnet{http://mi.mathnet.ru/semr682}
\crossref{https://doi.org/10.17377/semi.2016.13.033}
Linking options:
  • https://www.mathnet.ru/eng/semr682
  • https://www.mathnet.ru/eng/semr/v13/p375
  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Statistics & downloads:
    Abstract page:399
    Full-text PDF :73
    References:38
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024