Eigenvalues and energy of restricted unitary Cayley graphs induced from the square mapping

Abstract

Let R be a finite commutative ring with unity 1 6= 0. The restricted unitary Cayley graph induced from the squared mapping is the graph whose vertex set is R and whose edge set is {{a, b} : a, b ∈ R and a − b ∈ TR}, where TR = KR(R ×)2 and KR = {a ∈ R× : a = 1}. We study the structure of our graph HR and determine its eigenvalues and energy.