Some Properties of a Class of Addition Cayley Signed Graph

Abstract

Let [see formula in PDF] be a simple graph having vertex set [see formula in PDF]and edge set [see formula in PDF], where all [see formula in PDF] are distinct prime factors and [see formula in PDF] is the set of all units of the ring [see formula in PDF]be a signed graph whose underlying graph is [see formula in PDF] and signature function is [see formula in PDF] defined as [see formula in PDF]In this paper, we characterize the balance of [see formula in PDF] and some graphs derived from it such as [see formula in PDF], [see formula in PDF] and [see formula in PDF]. Moreover, we investigate the clusterability and sign-compativility of [see formula in PDF].