# (p,q)-Graceful signed graph

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$(p,q)$-Graceful signed graph --- $(p,q)$-грациозный знаковый граф.

Let $S = (G,s)$ be a sigraph and $s$ be a function which assigns a positive or a negative sign to each edge of $G$. Let the sets $E^{+}$ and $E^{-}$ consist of $m$ positive and $n$ negative edges of $G$, respectively, where $m+n = q$. Given positive integers $k$ and $d$, $S$ said to be $(k,d)$-graceful if the vertices of $G$ can be labeled with distinct integers from the set $\{0, 1, \ldots, k+(q-1)d\}$ such that, when each edge $uv$ of $G$ is assigned the product of its sign and the absolute difference of the integers assigned to $u$ and $v$, the edges in $E^{+}$ and $E^{-}$ are labeled with $k, k+d, k+2d, \ldots, k+(m-1)d$ and $-k, -(k+d), -(k+2d), \ldots, -(k+(n-1)d)$, respectively.