Unitary Addition Cayley Ring Signed Graphs *

Abstract

A signed graph (or sigraph in short) S is a graph G where the edges are weighted either + 1 or − 1 called the signs of the edges. Considering Zn′, the integers modulo n, where n is a positive integer greater than 1, special kind of structure called unitary addition Cayley graph denoted by Gn exists in the literature. On the unitary addition Cayley graph Gn, we define four different unitary addition Cayley sigraph denoted by , , and , by assigning the signs to the edges of Gn by a certain rule. The study in this paper concentrates on the discussion of one such signed structure called unitary addition Cayley ring sigraph, for different properties such as balancing, clusterability, canonically consistency and sign-compatibility.