Lattice Labelling of a Graph

Abstract

Let $G(u,v)$ be a connected graph. Let $ L = (L, \wedge,\vee) $ be a lattice under partial order $ \tau $. Let $ f:v\longrightarrow{L} $ be a injective function. Let $ f^\star:E\longrightarrow L'$ be the function induced by f such that $ f^\star(xy)= [f(x)\vee f(y)]-[f(x)\wedge f(y)]$ then we say f is a $ \tau $ labeling if L is injective and L' is a subset of L. A $ \tau $ labeling is called lattice labeling if L' is a sub lattice of L. In this paper we give lattice labeling of certain graphs.