On the Unitary Cayley Signed Graphs

A signed graph (or sigraph in short) is an ordered pair S = (S-u, sigma), where S-u is a graph G = (V, E) and sigma : E -> {+, -} is a function from the edge set E of S-u into the set {+, -}. For a positive integer n > 1, the unitary Cayley graph X-n is the graph whose vertex set is Z(n), the integers modulo n and if U-n denotes set of all units of the ring Z(n), then two vertices a, b are adjacent if and only if a - b is an element of U-n. For a positive integer n > 1, the unitary Cayley sigraph S-n = (S-n(u), sigma) is defined as the sigraph, where S-n(u) is the unitary Cayley graph and for an edge ab of S-n, sigma(ab) = {+ if a is an element of U-n or b is an element of Un, - otherwise. In this paper, we have obtained a characterization of balanced unitary Cayley sigraphs. Further, we have established a characterization of canonically consistent unitary Cayley sigraphs S-n, where n has at most two distinct odd prime factors.