New Results of Face Labeling for Some Plane Graphs

Abstract

A labeling of a plane graph is called super d-antimagic if the vertices receive the smallest labels and the weight set of all faces in an arithematic progression with difference d, where weight of each face is the some of all labels correspond to that face. In this paper, first we construct an upper bound for the paprmeter d. Secondly, we show that if a plane graph G is super d-antimagic then its subdivision is also super d-antimagic. Finally, we show that the Dutch windmill graph exist super d-antimagic labeling for different values of d, s.