Journal of Mathematical Chemistry

, Volume 41, Issue 1, pp 45–57 | Cite as

Some upper bounds for the energy of graphs

  • Huiqing Liu
  • Mei Lu
  • Feng Tian

Let G = (V,E) be a graph with n vertices and e edges. Denote V(G) = {v 1,v 2,...,v n }. The 2-degree of v i , denoted by t i , is the sum of degrees of the vertices adjacent to \(v_i, 1\leqslant i\leqslant n\). Let σ i be the sum of the 2-degree of vertices adjacent to v i . In this paper, we present two sharp upper bounds for the energy of G in terms of n, e, t i , and σ i , from which we can get some known results. Also we give a sharp bound for the energy of a forest, from which we can improve some known results for trees.


graph energy bipartite forest tree 


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Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.School of Mathematics and Computer ScienceHubei UniversityWuhanChina
  2. 2.Department of Mathematical SciencesTsinghua UniversityBeijingChina
  3. 3.Institute of Systems Science, Academy of Mathematics and Systems SciencesChinese Academy of SciencesBeijingChina

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