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IPM
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YEARS OLD

“School of Mathematics”

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Paper   IPM / M / 8728
School of Mathematics
  Title:   Choice number and energy of graphs
  Author(s): 
1.  S. Akbari
2.  E. Ghorbani
  Status:   Published
  Journal: Linear Algebra Appl.
  Vol.:  429
  Year:  2008
  Pages:   2687-2690
  Supported by:  IPM
  Abstract:
The energy of a graph G, denoted by E(G), is defined as the sum of the absolute values of all eigenvalues of G. It is proved that E(G) ≥ 2(nX(G)) ≥ 2(ch(G) − 1) for every graph G of order n, and that E(G) ≥ 2ch(G) for all graphs G except for those in a few specified families, where G, X(G), and ch(G) are the complement, the chromatic number, and the choice number of G, respectively.

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