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Domination in graphs with minimum degree two
Author(s) -
McCuaig William,
Shepherd Bruce
Publication year - 1989
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190130610
Subject(s) - combinatorics , mathematics , vertex (graph theory) , degree (music) , graph , dominating set , discrete mathematics , domination analysis , connectivity , physics , acoustics
The domination number γ( G ) of a graph G = ( V, E ) is the minimum cardinality of a subset of V such that every vertex is either in the set or is adjacent to some vertex in the set. We show that if a connected graph G has minimum degree two and is not one of seven exceptional graphs, then γ( G )γ 2/5| V |. We also characterize those connected graphs with γ( G )γ 2/5| V |.
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