Some Families of Tree Are Elegant

Abstract

An elegant labeling on the graph G with n vertex and m edge is a one-to-one mapping (injection function) of the vertex set V (G) to the set of non negative integers {0, 1, 2, 3, . . . , m} such that each edge gets the label of the sum from the adjacent vertex label in modulo number (m+1) all different and nonzero, that is: g(e) = g(uv) = [g(u)+g(v)] mod (m+ 1) and g(e) 6= 0, where u and v are adjacent vertices. In this research, we investigate the elegant labelling of selected graph from some families of tree. A tree graph is a graph that does not contain a circle. The selected some families of tree are generalized of star and amalgamation of star. The results of this research have shown that some families of tree graph are elegant