Magic labelings of triangles

The first proof is given that for every even integer s≥4s≥4, the graph consisting of ss vertex disjoint copies of C3C3, (denoted sC3sC3) is vertex-magic. Hence it is also edge-magic. It is shown that for each even integer s≥6s≥6, sC3sC3 has vertex-magic total labelings with at least 2s−22s−2 different magic constants. If s≡2mod4s≡2mod4, two extra vertex-magic total labelings with the highest possible and lowest possible magic constants are given. If s=2⋅3ks=2⋅3k, k≥1k≥1, it is shown that sC3sC3 has a vertex-magic total labeling with magic constant hh if and only if (1/2)(15s+4)≤h≤(1/2)(21s+2)(1/2)(15s+4)≤h≤(1/2)(21s+2). It is also shown that 2C32C3 is not vertex-magic. If ss is odd, vertex-magic total labelings for sC3sC3 with s+1s+1 different magic constants are provided.