Let \( G \) be a graph with vertex set \( V = V(G) \) and edge set \( E = E(G) \), and let \( n = |V(G)| \) and \( e = |E(G)| \). A \({vertex-magic\; total\; labeling}\) (VMTL) of a graph is defined as a one-to-one mapping taking the vertices and edges onto the set of integers \(\{1, 2, \ldots, n+e\}\), with the property that the sum of the label on a vertex and the labels on its incident edges is a constant independent of the choice of vertex. In this paper, we present the vertex-magic total labeling of the disjoint union of \( t \) generalized Petersen graphs \(\bigcup_{j=1}^t P(n_j, m_j)\), and the disjoint union of \( t \) special circulant graphs \(\bigcup_{j=1}^t C_n(1, m_j)\).