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Vertex criticality for upper domination and irredundance

✍ Scribed by P. J. P. Grobler; C. M. Mynhardt

Publisher: John Wiley and Sons
Year: 2001
Tongue: English
Weight: 104 KB
Volume: 37
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.1015

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✦ Synopsis

Abstract

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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