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 Diskretn. Anal. Issled. Oper., 2018, Volume 25, Issue 1, Pages 25–41 (Mi da888)

Tree-like structure graphs with full diversity of balls

A. A. Evdokimovab, T. I. Fedoryaevaab

a Sobolev Institute of Mathematics, 4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia
b Novosibirsk State University, 2 Pirogov St., 630090 Novosibirsk, Russia

Abstract: Under study is the diversity of metric balls in connected finite ordinary graphs considered as a metric space with the usual shortest-path metric. We investigate the structure of graphs in which all balls of fixed radius $i$ are distinct for each $i$ less than the diameter of the graph. Let us refer to such graphs as graphs with full diversity of balls. For these graphs, we establish some properties connected with the existence of bottlenecks and find out the configuration of blocks in the graph. Using the obtained properties, we describe the tree-like structure graphs with full diversity of balls. Illustr. 8, bibliogr. 22.

Keywords: graph, tree-like structure graphs, metric ball, radius of a ball, number of balls, diversity vector of balls, full diversity of balls.

 Funding Agency Grant Number Russian Academy of Sciences - Federal Agency for Scientific Organizations 0314-2015-0011

DOI: https://doi.org/10.17377/daio.2018.25.583

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English version:
Journal of Applied and Industrial Mathematics, 2018, 12:1, 19–27

UDC: 519.1+519.173
Revised: 08.08.2017

Citation: A. A. Evdokimov, T. I. Fedoryaeva, “Tree-like structure graphs with full diversity of balls”, Diskretn. Anal. Issled. Oper., 25:1 (2018), 25–41; J. Appl. Industr. Math., 12:1 (2018), 19–27

Citation in format AMSBIB
\Bibitem{EvdFed18} \by A.~A.~Evdokimov, T.~I.~Fedoryaeva \paper Tree-like structure graphs with full diversity of balls \jour Diskretn. Anal. Issled. Oper. \yr 2018 \vol 25 \issue 1 \pages 25--41 \mathnet{http://mi.mathnet.ru/da888} \crossref{https://doi.org/10.17377/daio.2018.25.583} \elib{https://elibrary.ru/item.asp?id=32729777} \transl \jour J. Appl. Industr. Math. \yr 2018 \vol 12 \issue 1 \pages 19--27 \crossref{https://doi.org/10.1134/S1990478918010039} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85043289729}