On the existence problem of the total domination vertex critical graphs

Title
On the existence problem of the total domination vertex critical graphs
Author(s)
이재운손무영[손무영]김동석[김동석]권영수
Keywords
DIAMETER
Issue Date
201101
Publisher
ELSEVIER SCIENCE BV
Citation
DISCRETE APPLIED MATHEMATICS, v.159, no.1, pp.46 - 52
Abstract
The existence problem of the total domination vertex critical graphs has been studied in a series of articles we first settle the existence problem with respect to the parities of the total domination number m and the maximum degree Delta for even m except m = 4 there is no m-gamma(iota) critical graph regardless of the parity of Delta for m = 4 or odd m >= 3 and for even Delta an m-gamma(iota)-critical graph exists if and only if Delta >= 2left perpendicular m-1/2 right perpendicular for m = 4 or odd m >= 3 and for odd Delta if Delta >= 2left perpendicular m-1/2 right perpendicular + 7 then m-gamma(iota)-critical graphs exist if Delta < 2left perpendicular m-1/2 right perpendicular then m-gamma(iota)-critical graphs do not exist The only remaining open cases are Delta = 2left perpendicular m-1/2 right perpendicular + k k = 1 3 5 Second we study these remaining open cases when m = 4 or odd m >= 9 As the previously known result for m = 3 we also show that for Delta(G) = 3 5 7 there is no 4-gamma(iota)-critical graph of order Delta (G) + 4 On the contrary it is shown that for odd m >= 9 there exists an m-gamma(iota)-critical graph for all Delta >= m - 1 (C) 2010 Elsevier B V All rights reserved
URI
http://hdl.handle.net/YU.REPOSITORY/25800http://dx.doi.org/10.1016/j.dam.2010.09.004
ISSN
0166-218X
Appears in Collections:
이과대학 > 수학과 > Articles
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