
doi: 10.37236/716
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 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 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 $\mathcal{S}_n$, $$\sigma(ab) = \begin{cases} + & \text{if } a \in U_n \text{ or } b \in U_n,\\ - & \text{otherwise.} \end{cases}$$ 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.
balanced unitary Cayley sigraphs, Structural characterization of families of graphs, Graphs and abstract algebra (groups, rings, fields, etc.), Signed and weighted graphs
balanced unitary Cayley sigraphs, Structural characterization of families of graphs, Graphs and abstract algebra (groups, rings, fields, etc.), Signed and weighted graphs
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