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Paper   IPM / M / 8726
School of Mathematics
  Title:   Some relations between rank, chromatic number and energy of graphs
1.  S. Akbari
2.  E. Ghorbani (Joint with S. Zare)
  Status:   To Appear
  Journal: Discrete Math.
  Supported by:  IPM
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) ≥ 2max(X(G),nX(G), where n is the number of vertices of G, G and X(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.

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