Wn-SUPER MAGIC LABELING ON GRAPH Pm ⊵e Wn

Abstract

Suppose G graph, H subgraph of G, then graph G admits H-covering having an H-magic labeling if there exist a bijective function mapping V (G) ∪ E(G) to a set of natural number at most |V (G)| + |E(G)| such that for any subgraph H¯ of G isomorphic to H, the sum of vertex and edge label of H¯ is equal to a fix number k, where k is a magic number. Moreover, such a labeling called H-super magic if the range of vertex set of G is a set positive integer less than or equal to |V (G)|. Suppose that e is an edge of Wn. Graph Pm ⊵e Wn is a graph obtained by taking a copy of graph Pm, |E(Pm)| copies of Wn, then identifying i-th edge of Pm to an edge e at i-th copy of Wn. In this paper, we construct the Wn-supermagic labeling of Pm ⊵e Wn.