Further results on distance magic labeling of graphs

Abstract

Let G=G(V, E) be a graph. If for each vertex v, sum of the labeling of the vertices which are at a distance D from v is constant, then such a labeling is said to be D-distance magic labeling and a graph G is said to be D-distance magic graph. In this paper, we study D-distance magic labeling of cycles, complete multipartite graphs, and star graphs. Also we obtain necessary and sufficient conditions for trees, n-star and join of two graphs to admit a distance magic labeling.