The Energy of a Graph: Old and New Results

Ivan Gutman ()
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Ivan Gutman: University of Kragujevac, Faculty of Science

A chapter in Algebraic Combinatorics and Applications, 2001, pp 196-211 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1007/978-3-642-59448-9_13

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