Bibliographic Details
| Title: |
Integral circulant graphs of prime power order with maximal energy |
| Authors: |
Sander, J.W.1 sander@imai.uni-hildesheim.de, Sander, T.2 t.sander@ostfalia.de |
| Source: |
Linear Algebra & its Applications. Dec2011, Vol. 435 Issue 12, p3212-3232. 21p. |
| Subjects: |
Cayley graphs, Integrals, Eigenvalues, Matrices (Mathematics), Mathematical optimization, Divisor theory, Set theory, Approximation theory |
| Abstract: |
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 and a set of divisors of in such a way that they have vertex set and edge set . Using tools from convex optimization, we analyze the maximal energy among all integral circulant graphs of prime power order and varying divisor sets . Our main result states that this maximal energy approximately lies between and twice this value. We construct suitable divisor sets for which the energy lies in this interval. We also characterize hyperenergetic integral circulant graphs of prime power order and exhibit an interesting topological property of their divisor sets. [Copyright &y& Elsevier] |
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| Database: |
Engineering Source |
