Let G =(V, E) be finite and simple graphs with vertex set V(G) and edge set E(G). A graph G is called super edge-magic if there exists a bijection f: V(G) ∪ E(G) → {1, 2, ⋯, |V(G)| + |E(G)|} and f(V(G)) = {1, 2, ⋯, |V(G)|} such that f(x) + f(xy) + f(y) is a constant for every edge xyE(G). A graph G with isolated vertices is called pseudo super edge-magic if there exists a bijection f: V(G) → {1, 2, ⋯, |V(G)|} such that the set {f(x) + f(y) ∶ xyE(G)} ∪ {2f(x) ∶ deg(x) = 0} consist of |E(G)| + |{xV(G) ∶ deg(x) = 0}| consecutive integers. In this paper, we construct (pseudo) super edge-magic 2-regular graphs from a super edge-magic cycle by using normalized Kotzig arrays. We also show that the graph C3CnK1 is pseudo super edge-magic for n ≡ 1(mod 4). By this result, we obtain some new classes of super edge-magic 2-regular graphs. In addition, we show that union of cycles and paths are super edge-magic.

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