THE ENERGY OF INTEGRAL CIRCULANT GRAPHS WITH PRIME POWER ORDER

被引：15
|
作者：
Sander, J. W. [1 ]
Sander, T. [2 ]
机构：
[1] Univ Hildesheim, Inst Math & Angew Informat, D-31141 Hildesheim, Germany
[2] Ostfalia Hsch Angew Wissensch, Fak Informat, D-38302 Wolfenbuttel, Germany
来源：
APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS | 2011年 / 5卷 / 01期
关键词：
Cayley graphs; integral circulant graphs; gcd graphs; graph energy; SPECTRA;
D O I：
10.2298/AADM110131003S
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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 Z(n) and its edge set is {{a, b} : a, b is an element of Z(n), gcd(a - b, n) is an element of D}. For an integral circulant graph on p(s) 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 p(s) and varying divisor sets D.
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页码：22 / 36
页数：15
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