Even vertex odd mean labeling of transformed trees

Abstract

Let G = (V;E) be a graph with p vertices and q edges. A graph G is said have an even vertex odd mean labeling if there exists a function f: V (G) →{0; 2; 4;:::; 2q} satisfying f is 1-1 and the induced map f*: E(G) → {1; 3; 5;:::; 2q-1g} defined by f*(uv) = f(u)+f(v)/2 is a bijection. A graph that admits even vertex odd mean labeling is called an even vertex odd mean graph. In this paper, we prove that Tp-tree (transformed tree), T@P���, T@2Pn and <T OK₁, n> (where T is a Tp-tree), are even vertex odd mean graphs.