The energy of integral circulant graphs with prime power order | Zendy

J. Sander | Zendy; Torsten Sander | Zendy

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The energy of integral circulant graphs with prime power order

Author(s) -

J. Sander,

Torsten Sander

Publication year - 2011

Publication title -

applicable analysis and discrete mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.69

H-Index - 26

eISSN - 2406-100X

pISSN - 1452-8630

DOI - 10.2298/aadm110131003s

Subject(s) - mathematics , circulant matrix , combinatorics , circulant graph , vertex (graph theory) , adjacency matrix , eigenvalues and eigenvectors , discrete mathematics , prime (order theory) , prime power , graph , line graph , graph power , physics , quantum mechanics

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. Such a graph can be characterized by its vertex count n and a set D of divisors of n such that its vertex set is Zn and its edge set is {{a,b} : a, b ? Zn; gcd(a-b, n)? D}. For an integral circulant graph on ps vertices, where p is a prime, we derive a closed formula for its energy in terms of n and D. Moreover, we study minimal and maximal energies for fixed ps and varying divisor sets D.

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