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The cohesiveness of a point of a graph
Author(s) -
Akiyama Jin,
Boesch Frank,
Era Hiroshi,
Harary Frank,
Tindell Ralph
Publication year - 1981
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.3230110107
Subject(s) - group cohesiveness , mathematics , combinatorics , graph , discrete mathematics , social psychology , psychology
The connectivity contribution or cohesiveness of a point v of graph G is defined as the difference k ( G ) ‐ k ( G ‐ v ) where kappa is the usual connectivity symbol. It is shown that if a point v of G has negative cohesiveness, then the set of points adjacent to v is the unique minimum size disconnecting set of G . This theorem has several corollaries including the result that if v has negative cohesiveness in G , then it does not in Γ. Finally we define a cohesiveness triple ( n_, n 0 , n + ) of a graph by taking these, respectively, as the number of negative, zero, and positive cohesiveness points of G . The necessary and sufficient conditions for an arbitrary triple to be the cohesiveness triple of a graph are derived.