Mathematics – Combinatorics
Scientific paper
2007-10-30
Cvetkovi\' c D., Grout J., Maximal energy graphs should have a small number of distinct eigenvalues, Bull. Acad. Serbe Sci. Ar
Mathematics
Combinatorics
17 pages; contains a SAGE program and minor grammatical corrections that are not contained in the published version
Scientific paper
The 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.
Cvetkovic Dragos
Grout Jason
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