The exact maximal energy of integral circulant graphs with prime power order
نویسندگان
چکیده
The energy of a graph was introduced by Gutman in 1978 as the sum of the absolute values of the eigenvalues of its adjacency matrix. We study the energy of integral circulant graphs, also called gcd graphs. These are Cayley graphs on cyclic groups (i.e. there adjacency matrix is circulant) each of whose eigenvalues is an integer. Given an arbitrary prime power p, we determine all integral circulant graphs of order p having maximal energy. This enables us to compute the maximal energy Emax(p) among all integral circulant graphs of order p.
منابع مشابه
Integral circulant graphs of prime power order with maximal energy
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 Zn and edge set {{a, b} : a, b ∈ Zn, gcd(a− b, n) ∈ D}. Using tools from convex optimization, we study the maxim...
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ورودعنوان ژورنال:
- Contributions to Discrete Mathematics
دوره 8 شماره
صفحات -
تاریخ انتشار 2013