SOME SPECIAL TYPES OF SQUARE DIFFERENCE GRAPHS
J. Shiama · 2012
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.