Cycle-magic graphs Original Research Article

A simple graph image admits a cycle-covering if every edge in E belongs at least to one subgraph of G isomorphic to a given cycle C. Then the graph G is C-magic if there exists a total labelling image such that, for every subgraph image of G isomorphic to C, image is constant. When image, then G is said to be C-supermagic. We study the cyclic-magic and cyclic-supermagic behavior of several classes of connected graphs. We give several families of image-magic graphs for each image. The results rely on a technique of partitioning sets of integers with special properties.