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2001 (2)
1Author    Ante Graovacab, Ivan Gutmanc, PeterE. Johnd, Dusica Vidovicc, Ivana VlahaRequires cookie*
 Title    On Statistics of Graph Energy  
 Abstract    The energy EG of a graph G is the sum of the absolute values of the eigenvalues of G. In the case whene G is a molecular graph, EG is closely related to the total ^-electron energy of the corresponding conjugated molecule. We determine the average value of the difference between the energy of two graphs, randomly chosen from the set of all graphs with n vertices and m edges. This result provides a criterion for deciding when two (molecular) graphs are almost coeneigetic. 
  Reference    Z. Naturforsch. 56a, 307—311 (2001); received January 26 2001 
  Published    2001 
  Keywords    Energy (of graph), Total jr-electron Energy, Coenergetic Graphs 
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 TEI-XML for    default:Reihe_A/56/ZNA-2001-56a-0307.pdf 
 Identifier    ZNA-2001-56a-0307 
 Volume    56 
2Author    Harald Fripertinger, Ivan Gutman3, Adalbert Kerber6, Axel Kohnertb, Dusica Vidovic3Requires cookie*
 Title    The Energy of a Graph and its Size Dependence. An Improved Monte Carlo Approach  
 Abstract    In an earlier work [Gutman et al., Chem. Phys. Lett. 297, 428 (1998)] the average energy (E) o f graphs with n vertices and m edges was examined, in particular its dependence on n and m . The quantity (E) was computed from a set of randomly, but not uniformly, constructed (n ,m)-graphs. We have now improved our method by constructing the (n,m)-graphs uniformly, so that every (n , m)-graph has equal probability to be generated. Differences between the old and new approaches are significant only in the case of graphs with a small number o f edges. 
  Reference    Z. Naturforsch. 56a, 342—346 (2001); received April 2 2001 
  Published    2001 
  Keywords    Energy (of Graph), Total 7r-electron Energy, Random Graphs, Monte Carlo Methods 
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 TEI-XML for    default:Reihe_A/56/ZNA-2001-56a-0342.pdf 
 Identifier    ZNA-2001-56a-0342 
 Volume    56