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Maximal energy bipartite graphsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2003 (English)In: Graphs and Combinatorics, ISSN 0911-0119, E-ISSN 1435-5914, Vol. 19, no 1, p. 131-135Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2003. Vol. 19, no 1, p. 131-135
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:miun:diva-13646DOI: 10.1007/s00373-002-0487-7ISI: 000182689700009Scopus ID: 2-s2.0-0038238082OAI: oai:DiVA.org:miun-13646DiVA: diva2:411881
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Available from: 2011-04-19 Created: 2011-04-19 Last updated: 2017-12-11Bibliographically approved

Given a graph G, its energy E(G) is defined to be the sum of the absolute values of the eigenvalues of G. This quantity is used in chemistry to approximate the total pi-electron energy of molecules and in particular, in case G is bipartite, alternant hydrocarbons. Here we show that if G is a bipartite graph with n vertices, thenE(G) less than or equal to n/(root8 (root2 + n)must hold, characterize those bipartite graphs for which this bound is sharp, and provide an infinite family of maximal energy bipartite graphs.Given a graph G, define the energy of G, denoted E(G), by[GRAPHICS]where the eigenvalues of, G are simply those of the adjacency matrix of G. In chemistry, the energy of a graph is intensively studied since it can be used to approximate, the total pi-electron energy of a molecule (see, for example, [3, 6, 8]). In [12], we considered maximal energy graphs (see also [9, 10, 13, 14, 17] for related results). In particular, for any graph G with n vertices, we derived an improvement of the well-known McClelland bound [15] for the energy of a graph, showing thatE(G) less than or equal to n/2(1 + rootn)must hold. We also characterized those graphs for which this bound is sharp, i.e. the maximal energy graphs, and provided an infinite family of such graphs.

doi
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