Energy of unitary Cayley graphs and gcd-graphs

Abstract

This work is based on ideas of Ilić [A. Ilić, The energy of unitary Cayley graphs, Linear Algebra Appl. 431 (2009) 1881–1889] on the energy of unitary Cayley graph. For a finite commutative ring R with unity 1 ≠ 0 , the unitary Cayley graph of R is the Cayley graph whose vertex set is R and the edge set is { { a , b } : a , b ∈ R and a - b ∈ R × } , where R × is the group of units of R. We study the eigenvalues of the unitary Cayley graph of a finite commutative ring and some gcd-graphs and compute their energy. Moreover, we obtain the energy for the complement of unitary Cayley graphs.