On Face Antimagic Labeling of Strong Face Plane Graphs

Let G = (V (G), E(G), F (G)) be a simple, finite, connected, plane graph with the vertex set V (G), the edge set E(G) and the face set F (G). A labeling of type (1, 1, 1) assigns labels from the set {1, 2, . . . , |V (G)|+ |E(G)| + |F (G)|} to the vertices, edges and faces of a plane graph G, such that each vertex, edge and face receives exactly one label and each number is used exactly once as a label. Moreover, the labeling is called super if the vertices are lebaled with the smallest numbers. The weight of a face under the labeling of type (1, 1, 1) is sum of labels of the face itself and vertices and edges surrounding that face. A labeling of a plane graph is called d-antimagic if for every positive integer s the set of weights of all s-sided faces is Ws={as, as + d, . . . , as + (νs − 1)d} for some integers as and d ≥ 0, where νs is the number of the s-sided faces. In this paper we study (super) d-antimagic labeling of type (1, 1, 1) for some strong face plane graphs. Mathematics Subject Classification: 05C78 78 Mohammed Ali Ahmed and J. Baskar Babujee