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The ultracenter and central fringe of a graph
Author(s) -
Chartrand Gary,
Novotny Karen S.,
Winters Steven J.
Publication year - 2001
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/net.1021
Subject(s) - combinatorics , mathematics , vertex (graph theory) , graph , neighbourhood (mathematics) , vertex connectivity , discrete mathematics , mathematical analysis
The central distance of a central vertex v in a connected graph G with rad G < diam G is the largest nonnegative integer n such that whenever x is a vertex with d ( v, x ) ≤ n then x is also a central vertex. The subgraph induced by those central vertices of maximum central distance is the ultracenter of G . The subgraph induced by the central vertices having central distance 0 is the central fringe of G . For a given graph G , the smallest order of a connected graph H is determined whose ultracenter is isomorphic to G but whose center is not G . For a given graph F , we determine the smallest order of a connected graph H whose central fringe is isomorphic to G but whose center is not G . © 2001 John Wiley & Sons, Inc.