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{\bf Deepa Sinha and Pravin Garg }
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{\bf On the Unitary Cayley Signed Graphs}
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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 \ $\sigma : E\rightarrow  \{+,-\}$ \ is a function from the edge set \ $E$ \ of \ $S^u$ \ into the set \ $\{+, -\}$. For a positive integer \ $n > 1$, the \emph{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 \ $a-b \in U_n$. For a positive integer \ $n > 1$, the \emph{unitary Cayley sigraph} \ $\mathcal{S}_n = (\mathcal{S}^u_n, \sigma)$ \ is defined as the sigraph, where \ $\mathcal{S}^u_n$ \ is the unitary Cayley graph and for an edge \ $ab$ \ of \ $\mathcal{S}_n$,
$$\sigma(ab) = \begin{cases}
+ & \text{if \ $a \in U_n$ \ or \ $b \in U_n$},\\
- & \text{otherwise.}
\end{cases}$$

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 \ $\mathcal{S}_n$, where \ $n$ \ has at most two distinct odd prime factors.

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