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Let \( a \) and \( b \) be two positive integers. For the graph \( G \) with vertex set \( V(G) \) and edge set \( E(G) \) with \( p = |V(G)| \) and \( q = |E(G)| \), we define two sets \( Q(a) \) and \( P(b) \) as follows:
\[
Q(a) = \begin{cases}
\{\pm a, \pm(a+1), \ldots, \pm(a + (q-2)/2)\} & \text{if } q \text{ is even,} \\
\{0\} \cup \{\pm a, \pm(a+1), \ldots, \pm(a + (q-3)/2)\} & \text{if } q \text{ is odd,}
\end{cases}
\]
\[
P(b) = \begin{cases}
\{\pm b, \pm(b+1), \ldots, \pm(b + (p-2)/2)\} & \text{if } p \text{ is even,} \\
\{0\} \cup \{\pm b, \pm(b+1), \ldots, \pm(b + (p-3)/2)\} & \text{if } p \text{ is odd.}
\end{cases}
\]
For the graph \( G \) with \( p = |V(G)| \) and \( q = |E(G)| \), \( G \) is said to be \( Q(a)P(b) \)-super edge-graceful (in short, \( Q(a)P(b) \)-SEG), if there exists a function pair \( (f, f^+) \) which assigns integer labels to the vertices and edges; that is, \( f^+: V(G) \to P(b) \), and \( f: E(G) \to Q(a) \) such that \( f^+ \) is onto \( P(b) \) and \( f \) is onto \( Q(a) \), and
\[
f^+(u) = \sum\{ f(u,v) : (u, v) \in E(G) \}.
\]
We investigate \( Q(a)P(b) \) super-edge-graceful labelings for three classes of \( (p,p+1) \)-graphs.