en>Headbomb: Various citation cleanup (identifiers mostly) using AWB

2011-09-05T07:01:59Z

Various citation cleanup (identifiers mostly) using AWB

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In [[mathematics]], the '''energy''' of a [[graph (mathematics)|graph]] is the sum of the [[absolute value]]s of the [[eigenvalue]]s of the [[adjacency matrix]] of the graph. This quantity is studied in the context of [[spectral graph theory]].

More precisely, let ''G'' be a graph with ''n'' [[vertex (graph theory)|vertices]]. It is assumed that ''G'' is [[Graph (mathematics)#Simple graph|simple]], that is, it does not contain loops or parallel edges. Let ''A'' be the [[adjacency matrix]] of ''G'' and let <math>\lambda_i</math>, <math> i = 1 , \ldots , n </math>, be the eigenvalues of ''A''. Then the energy of the graph is defined as:

:<math>E(G) = \sum_{i=1}^n|\lambda_i|.</math>

== References ==
*{{citation
| last1 = Cvetković | first1 = Dragoš M.
| last2 = Doob | first2 = Michael
| last3 = Sachs | first3 = Horst | author3-link = Horst Sachs
| isbn = 0-12-195150-2
| location = New York
| mr = 572262
| publisher = Academic Press Inc. [Harcourt Brace Jovanovich Publishers]
| series = Pure and Applied Mathematics
| title = Spectra of graphs
| volume = 87
| year = 1980}}.
*{{citation
| last = Gutman | first = Ivan
| contribution = The energy of a graph
| mr = 525890
| pages = 1–22
| series = Ber. Math.-Statist. Sekt. Forsch. Graz
| title = 10. Steiermärkisches Mathematisches Symposium (Stift Rein, Graz, 1978)
| volume = 103
| year = 1978}}.
*{{citation
| last = Gutman | first = Ivan
| contribution = The energy of a graph: old and new results
| location = Berlin
| mr = 1851951
| pages = 196–211
| publisher = Springer
| title = Algebraic combinatorics and applications (Gößweinstein, 1999)
| year = 2001}}.

[[Category:Algebraic graph theory]]

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Continuous Hahn polynomials - Revision history

en>Headbomb: Various citation cleanup (identifiers mostly) using AWB