Nordhaus-Gaddum-type Theorems for decompositions into many parts

Nordhaus-Gaddum-Type Theorem for Diameter of Graphs when Decomposing into Many Parts

A Note on Nordhaus-gaddum-type Inequalities for the Automorphic H-chromatic Index of Graphs

ing and Indexing: Zentralblatt MATH. AUTHORS INFO ARTICLE INFO JOURNAL INFO 2 Nordhaus-Gaddum-type inequalities

Nordhaus-Gaddum Problems for Colin de Verdière Type Parameters, Variants of Tree-width, and Related Parameters

A Nordhaus-Gaddum problem for a graph parameter is to determine a tight lower or upper bound for the sum or product of the parameter evaluated on a graph and on its complement. This article surveys Nordhaus-Gaddum results for the Colin de Verdière type parameters μ,ν , and ξ ; tree-width and its variants largeur d’arborescence, path-width, and proper path-width; and minor monotone ceilings of v...

Nordhaus-gaddum-type Relations for the Energy and Laplacian Energy of Graphs

A b s t r a c t. Let G denote the complement of the graph G . If I(G) is some invariant of G , then relations (identities, bounds, and similar) pertaining to I(G) + I(G) are said to be of Nordhaus-Gaddum type. A number of lower and upper bounds of Nordhaus-Gaddum type are obtained for the energy and Laplacian energy of graphs. Also some new relations for the Laplacian graph energy are established.

Nordhaus-Gaddum Type Results for Total Domination

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...