The maximal energy of classes of integral circulant graphs

  • Authors:

  • J. W. Sander;T. Sander

  • Affiliations:

  • Institut für Mathematik und Angewandte Informatik, Universität Hildesheim, D-31141 Hildesheim, Germany;Fakultät für Informatik, Ostfalia Hochschule für angewandte Wissenschaften, D-38302 Wolfenbüttel, Germany

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2012

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Abstract

The energy of a graph is the sum of the moduli of the eigenvalues of its adjacency matrix. We study the energy of integral circulant graphs, also called gcd graphs, which can be characterized by their vertex count n and a set D of divisors of n in such a way that they have vertex set Z"n and edge set {{a,b}:a,b@?Z"n,gcd(a-b,n)@?D}. For a fixed prime power n=p^s and a fixed divisor set size |D|=r, we analyse the maximal energy among all matching integral circulant graphs. Let p^a^"^1