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Vertex criticality for upper domination and irredundance
Author(s) -
Grobler P. J. P.,
Mynhardt C. M.
Publication year - 2001
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.1015
Subject(s) - combinatorics , mathematics , vertex (graph theory) , criticality , graph , critical exponent , discrete mathematics , physics , geometry , scaling , nuclear physics
Let π be any of the domination parameters ir γ, i , β, Γ or IR . The graph G is π‐ critical (π + ‐ critical ) if the removal of any vertex of G causes π( G ) to decrease (increase). We show that the classes of IR ‐critical and Γ‐critical graphs coincide, and exhibit a class of Γ + ‐critical graphs. © 2001 John Wiley & Sons, Inc. J Graph Theory 37: 205–212, 2001
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