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Maximal energy bipartite graphs
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
2003 (English)In: Graphs and Combinatorics, ISSN 0911-0119, E-ISSN 1435-5914, Vol. 19, no 1, 131-135 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2003. Vol. 19, no 1, 131-135 p.
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
Available from: 2011-04-19 Created: 2011-04-19 Last updated: 2016-10-24Bibliographically approved

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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
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  • de-DE
  • en-GB
  • en-US
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  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
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