Nordhaus-Gaddum Type Results for Total Domination
2011 ◽
Vol Vol. 13 no. 3
(Graph Theory)
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Keyword(s):
Graph Theory International audience A Nordhaus-Gaddum-type result is a (tight) lower or upper bound on the sum or product of a parameter of a graph and its complement. In this paper we study Nordhaus-Gaddum-type results for total domination. We examine the sum and product of γt(G1) and γt(G2) where G1 ⊕G2 = K(s,s), and γt is the total domination number. We show that the maximum value of the sum of the total domination numbers of G1 and G2 is 2s+4, with equality if and only if G1 = sK2 or G2 = sK2, while the maximum value of the product of the total domination numbers of G1 and G2 is max{8s,⌊(s+6)2/4 ⌋}.
2015 ◽
Vol Vol. 17 no. 1
(Graph Theory)
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2019 ◽
Vol 11
(01)
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pp. 1950004
2019 ◽
Vol 13
(07)
◽
pp. 2050129
2008 ◽
Vol Vol. 10 no. 1
(Graph and Algorithms)
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Keyword(s):
2010 ◽
Vol 4
(2)
◽
pp. 241-252
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Keyword(s):