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Some relations between rank, chromatic number and energy of graphs

Akbari, S ; Sharif University of Technology | 2009

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  1. Type of Document: Article
  2. DOI: 10.1016/j.disc.2008.09.012
  3. Publisher: 2009
  4. Abstract:
  5. The energy of a graph G, denoted by E (G), is defined as the sum of the absolute values of all eigenvalues of G. Let G be a graph of order n and rank (G) be the rank of the adjacency matrix of G. In this paper we characterize all graphs with E (G) = rank (G). Among other results we show that apart from a few families of graphs, E (G) ≥ 2 max (χ (G), n - χ (over(G, -))), where n is the number of vertices of G, over(G, -) and χ (G) are the complement and the chromatic number of G, respectively. Moreover some new lower bounds for E (G) in terms of rank (G) are given. © 2008 Elsevier B.V. All rights reserved
  6. Keywords:
  7. Chromatic number ; Energy ; Rank ; Absolute values ; Adjacency matrices ; Chromatic number ; Eigen values ; Energy ; Energy of a graphs ; Energy of graphs ; Lower bounds ; Rank ; Control theory
  8. Source: Discrete Mathematics ; Volume 309, Issue 3 , 2009 , Pages 601-605 ; 0012365X (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S0012365X08005402