Graphs with extremal energy should have a small number of distinct eigenvalues

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dc.creatorCvetkovic, Dragos
dc.creatorGrout, Jason
dc.date2007-10-30
dc.date.accessioned2026-07-07T08:39:29Z
dc.date.available2026-07-07T08:39:29Z
dc.descriptionThe sum of the absolute values of the eigenvalues of a graph is called the energy of the graph. We study the problem of finding graphs with extremal energy within specified classes of graphs. We develop tools for treating such problems and obtain some partial results. Using calculus, we show that an extremal graph ``should'' have a small number of distinct eigenvalues. However, we also present data that shows in many cases that extremal graphs can have a large number of distinct eigenvalues.
dc.description17 pages; contains a SAGE program and minor grammatical corrections that are not contained in the published version
dc.identifierhttps://arxiv.org/abs/0710.5669
dc.identifierhttp://arxiv.org/abs/0710.5669
dc.identifierCvetkovi\' c D., Grout J., Maximal energy graphs should have a small number of distinct eigenvalues, Bull. Acad. Serbe Sci. Arts, Cl. Sci. Math. Natur., Sci. Math., 134(2007), No. 32, 43-57
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/141090
dc.subjectCombinatorics
dc.subject05C50
dc.titleGraphs with extremal energy should have a small number of distinct eigenvalues
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