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On the existence problem of the total domination vertex critical graphs

✍ Scribed by Moo Young Sohn; Dongseok Kim; Young Soo Kwon; Jaeun Lee

Book ID: 108112901
Publisher: Elsevier Science
Year: 2011
Tongue: English
Weight: 259 KB
Volume: 159
Category: Article
ISSN: 0166-218X
DOI: 10.1016/j.dam.2010.09.004

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## Abstract A graph is __k__‐domination‐critical if γ(__G) = k__, and for any edge __e__ not in __G__, γ(__G + e) = k__ − 1. In this paper we show that the diameter of a domination __k__‐critical graph with __k__ ≧ 2 is at most 2__k__ − 2. We also show that for every __k__ ≧ 2, there is a __k__‐dom