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R. Frucht, “Graphs of degree three with a given abstract group,” Canadian Journal Mathematics, Vol. 1, pp. 365–378, 1949.

has been cited by the following article:

• TITLE: Frucht Graph is not Hyperenergetic

  AUTHORS: S. PIRZADA

  KEYWORDS: energy of a graph, hyperenergetic, frucht graph, automorphism

  JOURNAL NAME: Intelligent Information Management, Vol.1 No.2, November 30, 2009

  ABSTRACT: If are the eigen values of a p-vertex graph , the energy of is . If , then is said to be hyperenergetic. We show that the Frucht graph, the graph used in the proof of well known Frucht’s theorem, is not hyperenergetic. Thus showing that every abstract group is isomorphic to the automorphism group of some non-hyperenergetic graph. AMS Mathematics Subject Classification: 05C50, 05C35