On Magic Labelings of Graphs and Their Products

Abstract

For any graph G if there is a bijection exist from the set of vertices to collection of positive numbers such that every vertex’s open neighbourhood added together equals K is known as distance magic labeling, where K is distance magic constant. If a bijection exist from a nodes set to an abelian group for any graph G such that the sum of every open neighbor- hood of each vertex is a same number is known as group distance magic labeling . In this thesis we calculate the Distance Magic Labeling of P2 × Km,n, Km,n × Kp,q and C3 ×Km,n and also we have compute Group Distance Magic Labeling of Pm × Pn under abelian group Zmn.