A survey of Nordhaus-Gaddum type relations
نویسندگان
چکیده
In 1956, Nordhaus and Gaddum gave lower and upper bounds on the sum and on the product of the chromatic number of a graph and its complement, in terms of the order of the graph. Since then, relations of a similar type have been proposed for many other graph invariants, in several hundred papers. We present a survey on this research endeavor.
منابع مشابه
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.
متن کاملA 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
متن کاملNordhaus-Gaddum type results for the Harary index of graphs
The emph{Harary index} $H(G)$ of a connected graph $G$ is defined as $H(G)=sum_{u,vin V(G)}frac{1}{d_G(u,v)}$ where $d_G(u,v)$ is the distance between vertices $u$ and $v$ of $G$. The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalization of the concept of classical graph distance. For a connected graph $G$ of order at least $2$ ...
متن کاملNordhaus-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...
متن کاملNordhaus-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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discrete Applied Mathematics
دوره 161 شماره
صفحات -
تاریخ انتشار 2013