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 W s ={a s , a s + d,. .. , a s + (ν s − 1)d} for some integers a s and d ≥ 0, where ν s 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.

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The Wiener index is a topological index defined as the sum of distances between all pairs of vertices in a graph. It was introduced as a structural descriptor for molecular graphs of alkanes, which are trees with vertex degrees of four at the most. The terminal Wiener index is defined as the sum of distances between all pairs of pendent vertices in a graph. In this paper we investigate Wiener and terminal Wiener for graphs derived from certain operations.