Choice Number and Energy of Graphs
Combinatorics
2007-12-07 v1
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(n-\chi(\bar{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 \bar{G}, \chi(G), and ch(G) are the complement, the chromatic number, and the choice number of G, respectively.
Keywords
Cite
@article{arxiv.0712.0920,
title = {Choice Number and Energy of Graphs},
author = {Saieed Akbari and Ebrahim Ghorbani},
journal= {arXiv preprint arXiv:0712.0920},
year = {2007}
}
Comments
to appear in Linear Algebra and its Applications