TY - JOUR

T1 - Tree-Like Structure Graphs with Full Diversity of Balls

AU - Evdokimov, A. A.

AU - Fedoryaeva, T. I.

N1 - Publisher Copyright: © 2018, Pleiades Publishing, Ltd.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

KW - diversity vector of balls

KW - full diversity of balls

KW - graph

KW - metric ball

KW - number of balls

KW - radius of a ball

KW - tree-like structure graph

UR - http://www.scopus.com/inward/record.url?scp=85043289729&partnerID=8YFLogxK

U2 - 10.1134/S1990478918010039

DO - 10.1134/S1990478918010039

M3 - Article

AN - SCOPUS:85043289729

VL - 12

SP - 19

EP - 27

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 1

ER -