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) →2X, 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.