EMIS ELibM Electronic Journals Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiques
Vol. CXXXIV, No. 32, pp. 1–11 (2007)

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Nordhaus-Gaddum-type relations for the energy and Laplacian energy of graphs

B. Zhou and I. Gutman

Department of Mathematics, South China Normal University, Guangzhou 510631, P. R. China
Faculty of Science, University of Kragujevac, P. O. Box 60, 34000 Kragujevac, Serbia

Abstract: Let $\overline{G}$ denote the complement of the graph $G$ . If $I(G)$ is some invariant of $G$ , then relations (identities, bounds, and similar) pertaining to $I(G)+I(\overline{G})$ 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.

Keywords: spectrum (of graph), Laplacian spectrum (of graph), energy (of graph), Laplacian energy (of graph), Nordhaus-Gaddum-type relation

Classification (MSC2000): 05C50

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Electronic fulltext finalized on: 23 Sep 2007. This page was last modified: 20 Jun 2011.

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