• EDGE TRIMAGIC GRACEFUL LABELING OF SOME GRAPHS

Abstract

A (p, q) graph G is called edge trimagic total if there exists a bijection f: V(G) È E(G) ® {1, 2, 3, …, p+q} such that for each edge xy in E(G) the value of  f(x) + f(xy) + f(y) = K₁ or K₂ or K₃. G is called edge trimagic graceful if there exists a bijection f : V(G) È E(G) ® {1, 2, 3, …, p+q} such that for each edge xy in E(G), | f(x) – f(xy) + f(y) | = C₁ or C₂ or C₃, where C₁, C₂  and C₃ are constants. In this paper, we proved that the Umbrella graph U_n, _m, circular ladder graph CL(n) and the Dumbbell graph Db_n are edge trimagic graceful graphs.