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The exact maximal energy of integral circulant graphs with prime power order
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The energy of a graph was introduced by {\sc 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, 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/nZ and edge set {{a,b}:a,b∈Z/nZ,gcd(a−b,n)∈D}.
Given an arbitrary prime power ps, we determine all divisor sets maximising the energy of an integral circulant graph of order ps. This enables us to compute the maximal energy \Emaxps among all integral circulant graphs of order ps.
Title: The exact maximal energy of integral circulant graphs with prime power order
Description:
The energy of a graph was introduced by {\sc 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, 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/nZ and edge set {{a,b}:a,b∈Z/nZ,gcd(a−b,n)∈D}.
Given an arbitrary prime power ps, we determine all divisor sets maximising the energy of an integral circulant graph of order ps.
This enables us to compute the maximal energy \Emaxps among all integral circulant graphs of order ps.
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