Magic Labeling Of Type (1, 1, 1)

Abstract

In this thesis we have combined the ideas about the graphs and the labeling of the graphs. We have discussed the size of graph, order of graph, degree of vertex, kinds of vertex, kinds of edge, kinds of graph and some operations on graphs. The main focus of the thesis is on the magic labeling of type (a, b, c) for some families of graphs and for their subdivisions. A labeling is a map that carries set of graph elements to numbers (usually positive or non negative integers). We have defined vertex labeling, edge labeling and total labeling. We label the plane graph in such a way that label of a face and label of vertices and edges surrounding that face add up to a weight of face. The weight of a face under a labeling of type (a, b, c) is the sum of labels (if present) carried by that face and edges and vertices surrounding it. Moreover, the basic concepts of face labeling along with magic graphs, super-magic graphs and prime graphs are also discussed. In the end of this thesis we have define the magic labeling for some graphs. We also have formulated the magic labeling of type (a, b, c) for those graphs and for their subdivision.