Bitopological Harmonious Labeling of Some Star Related Graphs

Bitopological harmonious labeling for a graph G=(V(G),E(G)) with n vertices, is an injective function f:V(G)→2^X, where X is any non – empty set such that |X|=m,m< n and {f(V(G))} forms a topology on X, that induces an injective function f^*: E(G) → 2^(X^* ), defined by f^* (uv) = f(u)∩f(v) for every uv∈E(G) such that {f^* (E(G))} forms a topology on X^* where X^*=X\{1,2,….,m}. A graph that admits bitopological harmonious labeling is called a bitopological harmonious graph. In this paper, we discuss bitopological harmonious labeling of some star related graphs.