Cyclic Super Magic Labelings for Toroidal and Klein-Bottle Fullerenes

A simple graph G = (V, E) admits a cycle-covering if every edge in E belongs at least to one subgraph of G isomorphic to a given cycle C. The graph G is C-magic if there exists a total labeling f : V ∪ E → {1, 2, 3, ..., |V | + |E|} such that for every subgraph H' = (V', E') of G isomorphic to C, Σ
_V∈V'
f(V) + Σ
_E∈E'
f(E) is constant, when f(V) = 1, 2, 3, ..., |V|. Then G is said to be C-supermagic. In the present paper, we investigate the cyclic-supermagic behavior of toroidal and Klein-bottle graph.