Open AccessThe energy of integral circulant graphs with prime power order
Author(s) -
J. W. 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.