Topological Cordial Labeling of Some Graphs

Abstract

A topological cordial labeling of a graph G = (V(G), E(G)) with |V(G)| = n is an injective function f :V(G) →2^X where X is any non – empty set such that |X| < n and {f(V(G))} forms a topology on X, that induces a function f*: E(G) →{0,1} defined by f*(uv) = 1 if f(u)∩f(v) is not an empty set and not a singleton set and 0 otherwise for all uv ϵ E(G) such that |e_f (0) – e_f (1)| ≤ 1, where e_f (0) = number of edges labelled with 0 and e_f (1) = number of edges labelled with 1. The graph which admits a topological cordial labeling is called a topological cordial graph. In this paper, topological cordial labeling of some special graphs are discussed.