Vertex-Magic Total Labeling Algorithms on Unicycle Graphs and Some Graphs Related to Wheels

Let G be a graph with vertex set V and edge set E, where |V| and |E| be the number of vertices and edges of G. A bijection λ : V È E ® {1, 2, …, |V| + |E|} is called a vertex-magic total labeling if there is a constant k so that the weight of vertex x, wλ(x) = λ(x) + åyÎN(x) λ(xy) = k, for all x in V where N(x) is the set of vertices adjacent to x. This paper gives algorithms to generate all vertex-magic total labelings on some classes of unicycle graphs (suns and tadpoles) and some classes of graph related to wheels (friendships, fans, generalized Jahangirs). Using those algorithms, we enumerate all non isomorphic vertex-magic total labelings on those classes of graphs for some values of |V|.