Nordhaus-Gaddum-type theorem for Wiener index of graphs when decomposing into three parts

Authors:
Daobin Li;Baoyindureng Wu;Xunuan Yang;Xinhui An
Affiliations:
-;-;-;-
Venue:
Discrete Applied Mathematics
Year:
2011

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Abstract

Let K"n be the complete graph of order n. Assume that (G"1,G"2,G"3) is a 3-decomposition of K"n such that G"i is connected for each i=1,2,3. Then for any sufficiently large n, 5n2@?@?i=13W(G"i)@?n^3-n3+n2+2(n-1). We also prove that both bounds are best possible.