Algorithms for Inner Magic and Inner Antimagic Labelings of Some Planar Graphs

In this work labeling of planar graphs is taken up which involves labeling the p vertices, the q edges and the f internal faces such that the weights of the faces form an arithmetic progression with common difference d. If d = 0, then the planar graph is said to have an Inner Magic labeling; and if d = 0, then it is Inner Antimagic labeling. Some new kinds of graphs have been developed which have been derived from Wheels by adding vertices in a certain way and it is proposed to give new names to these graphs namely Flower-1 and Flower-2. This paper presents the algorithms to obtain the Inner Magic and Inner Antimagic labeling for Wheels and the Inner Antimagic labeling for Flower-1 and Flower-2. The results thus found show much regularity in the labelings obtained.