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The Energy of a Graph: Old and New Results

  • Ivan Gutman

Abstract

Let G be a graph possessing n vertices and m edges. The energy of G, denoted by E = E(G), is the sum of the absolute values of the eigenvalues of G. The connection between E and the total electron energy of a class of organic molecules is briefly outlined. Some (known) fundamental mathematical results on E are presented: the relation between E(G) and the characteristic polynomial of G, lower and upper bounds for E, especially those depending on n and m, graphs extremal with respect to E, n-vertex graphs for which E(G) > E(K n ). The characterization of the n-vertex graph(s) with maximal value of E is an open problem.

Keywords

Bipartite Graph Characteristic Polynomial Variable Neighborhood Search Complete Bipartite Graph Molecular Orbital Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Ivan Gutman
    • 1
  1. 1.Faculty of ScienceUniversity of KragujevacYugoslavia

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