Tree-Like Structure Graphs with Full Diversity of Balls

Tree-Like Structure Graphs with Full Diversity of Balls Full article

Journal

Journal of Applied and Industrial Mathematics
ISSN: 1990-4789 , E-ISSN: 1990-4797

Output data

Year: 2018, Volume: 12, Number: 1, Pages: 19-27 Pages count : 9 DOI: 10.1134/S1990478918010039

Tags

graph; tree-like structure graph, metric ball, radius of a ball, number of balls, diversity vector of balls, full diversity of balls

Authors

Evdokimov A.A. ^1,2 , Fedoryaeva T.I. ^1,2

Affiliations

1	Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russian Federation
2	Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russian Federation

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. © 2018, Pleiades Publishing, Ltd.

Evdokimov A.A. , Fedoryaeva T.I.
Tree-Like Structure Graphs with Full Diversity of Balls
Journal of Applied and Industrial Mathematics. 2018. V.12. N1. P.19-27. DOI: 10.1134/S1990478918010039 Scopus РИНЦ MathNet OpenAlex

Евдокимов А.А. , Федоряева Т.И.
Графы древовидной структуры с полным разнообразием шаров
Дискретный анализ и исследование операций. 2018. Т.25. №1. С.25-41. DOI: 10.17377/daio.2018.25.583 РИНЦ MathNet

Submitted:	Jun 27, 2017
Published print:	Mar 8, 2018

Scopus:	2-s2.0-85043289729
Elibrary:	35519978
MathNet:	eng/da888
OpenAlex:	W2791571167

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