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On eccentric vertices in graphs
Author(s) -
Chartrand Gary,
Schultz Michelle,
Winters Steven J.
Publication year - 1996
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/(sici)1097-0037(199612)28:4<181::aid-net2>3.0.co;2-h
Subject(s) - combinatorics , vertex (graph theory) , mathematics , graph , eccentricity (behavior) , connectivity , physics , political science , law
The eccentricity e ( v ) of a vertex v in a connected graph G is the distance between v and a vertex furthest from v . The minimum eccentricity among the vertices of G is the radius rad G of G , and the maximum eccentricity is its diameter diam G . A vertex u of G is called an eccentric vertex of v if d ( u, v ) = e ( v ). The radial number m( v ) of v is the minimum eccentricity among the eccentric vertices of v , while the diametrical number dn( v ) of v is the maximum eccentricity among the eccentric vertices of v . The radial number m( G ) of G is the minimum radial number among the vertices of G and the diametrical number dn( G ) of G is the minimum diametrical number among the vertices of G . Several results concerning eccentric vertices are presented. It is shown that for positive integers a and b with a ≤ b ≤ 2 a there exists a connected graph G having m( G ) = a and dn( G ) = b . Also, if a, b , and c are positive integers with a ≤ b ≤ c ≤ 2 a , then there exists a connected graph G with rad G = a , m( G ) = b , and diam G = c . © 1996 John Wiley & Sons, Inc.