On Topological Cordial Labeling of Some Graphs

Let G be the graph. A topological cordial labeling of a graph G with |V (G)| = n is an injective function f from the vertex set V(G) to the set 2X where X is a nonempty set such that |X| < n and it forms a topology on X, denoted by {f (V (G))}, that induced a function f ∗ from E (G) → {0, 1} defined by f ∗ (uv) = {1 0 if f (u) ∩ f (v)is not an empty set and not a singleton set, 0 otherwise for all uv ∈ E (G) such that |ef (0) − ef (1) | ≤ 1 where ef (0) is the number of vertices labeled with 0 and where ef (1) is the number of vertices labeled with 1. The graph that satisfies the condition of a topological cordial labeling is called topological cordial graph.