At most edge 3-sum cordial labeling for some graphs the standard

Let G =(V, E) be a graph of order n and size m. An edge labeling function f: E(G) ↠ (0, 1, 2) induces a vertex labeling function f: V(G) ↠ (0, 1, 2) defined as, (mod3), where e_i ∈ E(G) and e_i is incident to v_j, for each j = 0, 1, 2,…, (n-1). Then the map f is called Edge 3-sum cordial labeling if |v_f(i)-v_f(j)| < 1 and |e_f(i)-e_f(j)| < 1 for i ≠ j and i, j ∈ (0, 1, 2), where v_f (x) and e_f(x) denote the number of vertices and edges labeled with x, x ∈ (0, 1, 2). An edge 3-sum cordial graph which admits an edge sum cordial labeling is called at most edge 3-sum cordial labeling. A graph having at most edge 3-sum cordial labeling is called at most edge 3-sum cordial graph. In this paper, we prove that some standard graphs and special graphs like Gear graph, Double star and Friendship graph are at most edge 3-sum cordial graphs.