• SOME SPECIAL TYPES OF SQUARE DIFFERENCE GRAPHS

Abstract

I defined a new labeling and a new graph called square difference labeling and the square difference graph. Let G be a (p, q) graph. G is said to be a square difference graph if there exists a bijection f: V(G) →{ 0,1, …., p-1} such that the induced function f* : E(G) → N given by f*(uv) =| [f(u)]2 - [f(v)]2| for every uv ∈ E(G) are all distinct. A graph which admits square difference labeling is called square difference graph. I discussed the square difference labeling for some graphs like cycles, complete graphs, cycle cactus, ladder, lattice grids and wheels. In this paper my discussion is some graphs like mK3, mCn , path union of some K3, some Cn graphs and duplication of vertices by an edge to some star graphs ans crown graphs are square difference graphs. Also proved a path is an Odd square difference graph and star is a perfect square difference graph.