Topological Cordial Labeling for Some Different Types of Graphs

Abstract

For a graph G, topological cordial labeling for G is an injective function f:V(G)→2^X, X is a non – empty set such that |V(G)| > |X| that induces a function f^*:E(G) →{0,1} defined as f^* (uv)=0 if f(u)∩f(v) is an empty set or a singleton set and 1 otherwise for all edges in G such that 〖|e〗_f (0)-e_f (1)| is atmost 1 where e_f (1) denotes number of edges labelled with 1 and e_f (0) denotes the number of edges labelled with 0. Also {f(V(G))} forms a topology on X. The graph which admits a topological cordial labeling is called a topological cordial graph. In this paper, we discuss topological cordial labelling for some different types of graphs.