On Face Magic Labeling of Duplication Graphs

A labeling of a graph G of type assigns labels from the set to the vertices, edges and faces of G such that each vertex receives a label(s), each edge receives b label(s) and each face receives c label(s) and each number is used exactly once as a label. We restrict a, b and c to be not greater than one. The weight of face w(f) under a labeling is the sum of labels of the face itself together with labels of vertices and edges surrounding that face. A labeling is said to be magic, if for every positive integer s, all s-sided faces have the same weight. In this paper, we examine whether vertex and edge duplication on some families of graphs admit face magic labeling of types (1, 0, 1), (1, 1, 0), (0, 1, 1) and (1, 1, 1).