Geometric Mean Cordial Labeling of Transformation Graph of a Star Graph

Abstract

Let G = ( V, E ) be a graph and f be a mapping from V(G) → { 0, 1, 2 }. For each edge uv, assign the label  f (u) f (v) , f is called a geometric mean cordial labeling if | vf(i) − vf(j) | ≤ 1 and | ef(i) − e f(j) | ≤ 1,where vf (x) and ef (x) denote the number of vertices and edges labeled with x, x  { 0, 1, 2 } respectively. A graph with a geometric mean cordial labeling is called geometric mean cordial graph. In this paper, the geometric mean cordiality of transformation graph of star is discussed.