journal6 ›› 2012, Vol. 33 ›› Issue (5): 46-50.DOI: 10.3969/j.issn.1007-2985.2012.05.012

• Physics and electronics • Previous Articles     Next Articles

New Tree-Field Representations in Graph Theory and Extension of Dirac Extraction


  1. (Department of Physics,Yunnan University,Kunming 650091,China)
  • Online:2012-09-25 Published:2012-11-30

Abstract: The tree in the graph theory is extended to a new tree-field representation.It includes two parts:tree and field.A field is a set of legion small trees.There can be transformation between tree and field,which is a unification of simplicity (tree) and complexity (field),and may be applied to various complex systems on science,politics,economy,philosophy,history and so on.Further more,it may be extended to the whole graph theory G=(V,E,F),where F is a set of small graphs.Next,it is researched that the integral representations in physical theories are unified and the Dirac extraction is extended to any terms A2=B2+C2+D2+… whose extraction should be A=αB+βC+γD+… and α2=β2=γ2=…=1,etc.Finally,the general complexity is searched.

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