Unitary Cayley Meet Signed Graphs

A signed graph S is a graph in which every edge receive either '+' or '-' called the signs of the edges. The unitary Cayley graph Xn is a graph with vertex set Zn, the integers modulo n, where n is a positive integer greater than 1. Two vertices x1 and x2 are adjacent in the unitary Cayley graph if and only if their difference is in Un, where Un denotes set of all units of the ring Zn. The properties of balancing and clusterability of unitary Cayley meet signed graph Sn∧ are discussed. Apart from this, the canonically consistency of Sn∧ is determined when n has at most two distinct odd prime factors. Sign-compatibility has been worked out for these graphs as well.