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Some nordhaus-- gaddum-type results

✍ Scribed by Wayne Goddard; Michael A. Henning; Henda C. Swart

Publisher
John Wiley and Sons
Year
1992
Tongue
English
Weight
500 KB
Volume
16
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

A Nordhaus‐‐Gaddum‐type result is a (tgiht) lower or upper bound on the sum or product of a parameter of a graph and its complement. In this paper some variations are considered. First, the sums and products of ψ(G~1~) and ψ(G~2~) are examined where G~1~ ⊕ G~2~ = K(s, s), and ψ is the independence, domination, or independent domination number, inter alia. In particular, it is shown that the maximum value of the product of the domination numbers of G~1~ and G~2~ is [(s/2 + 2)^2^] for s ≥ 3. Thereafter it is shown that for H~1~ ⊕ H~2~ ⊕ H~3~ = K~p~, the maximum product of the domination numbers of H~2~, H~2~, and H~3~ is p^3^/27 + Θ(p^2^).

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