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A new technique is given for constructing a vertex-magic total labeling, and hence an edge-magic total labeling, for certain finite simple \(2\)-regular graphs. Let \( C_r \) denote the cycle of length \( r \). Let \( n \) be an odd positive integer with \( n = 2m + 1 \). Let \( k_i \) denote an integer such that \( k_i \geq 3 \), for \( i = 1, 2, \ldots, l \), and write \( nC_{k_i} \) to mean the disjoint union of \( n \) copies of \( C_{k_i} \). Let \( G \) be the disjoint union \( G \cong C_{k_1} \cup \ldots \cup C_{k_l} \). Let \( I = \{1, 2, \ldots, l\} \) and let \( J \) be any subset of \( I \). Finally, let \( G_J = \left(\bigcup_{i \in J} nC_{k_i}\right) \cup \left(\bigcup_{i \in I – J} C_{nk_i}\right) \), where all unions are disjoint unions. It is shown that if \( G \) has a vertex-magic total labeling (VMTL) with a magic constant of \( h \), then \( G_J \) has VMTLs with magic constants \( 6m(k_1 + k_2 + \ldots + k_l) + h \) and \( nh – 3m \). In particular, if \( G \) has a strong VMTL then \( G_J \) also has a strong VMTL.
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