(s, d) Magic Labeling of some ladder graphs

Abstract

Let G(p, q) be a connected, undirected, simple and non-trivial graph with q nodes and q lines. Let f be an injective function f: V(G) →{ s, s + d, s + 2d,.....s + (q +1)d } and g be an injective function g: E(G) → {d,2d,3d,… 2(q-1)d}.Then the graph G is said to be (s, d) magic labeling if f(u) + g(uv) + f(v) is a constant, for all u, v; ∈ V(G). A graph G is called (s, d) magic graph if it admits (s, d) magic labeling. In this paper the existence of (s, d) magic labeling in some ladder graphs are found.