3-Equitable Ceiling Average Labeling

Let T = (V, E) represent a graph where V is the set of vertices and E is the set of edges. Consider a labeling of the vertices f : V(T)→{0,1,2, ….., n-1} such that each edge e=uv is assigned a label ⌈  ⌉mod3. Then we say graph T admits 3-equitable Ceiling Average Labeling if  |vf (i)-vf (j)|≤1 and |ef (i)-ef (j)|≤ 1 for all 0 ≤ i, j ≤2. A graph which admits 3-equitable Ceiling Average Labeling is called a 3-equitable Graph. In this paper we have discussed the labeling of cycle graph, path graph, star graph and wheel graph. This labeling pattern can be applied in Traffic Flow Optimization, Power Grid Balancing, Data Clustering in Machine Learning.