GAUSSIAN SD-DIVISOR LABELING OF GRAPHS

Let G = (V (G), E(G)) be a simple, finite and undirected graph of order n.Given a bijection f : V (G) → [γn], we associate two Gaussian integersS = f (u)+f (v) and D = f (u)−f (v) or f (v)−f (u) with every edge uv in E(G).The labeling f induces on edge labeling f r : E(G) → {0, 1}, such that forevery edge uv in E(G), f r(uv) = 1 if D | S and f r(uv) = 0 if D - S. Let efr (i)be the number of edges labeled with i ∈ {0, 1}. The labeling f is calledan Gaussian SD-divisor labeling if f r(uv) = 1 for all uv ∈ E(G). A graphwhich admits Gaussian SD-divisor labeling is called Gaussian SD-divisorgraph. The labeling f is called an Gaussian SD-divisor cordial labeling if|efr (0) − efr (1)| ≤ 1. We say that G is Gaussian SD-divisor cordial ifit admits an Gaussian SD-divisor cordial labeling. In this paper, wedefine SD-divisibility and SD-divisor pair of Gaussian integers andestablish some of its properties. Also, we will find out some path and cyclerelated graphs are Gaussian SD-divisor and some standard graphs such asstar, complete, complete bipartite and wheel graphs which are not GaussianSD-divisor.