Odd mean labeling of TôCn andTõCn

Abstract

Let G = (V,E)be a graph with p vertices and q edges. A graph Gis said to be odd mean if there exists a function f:V(G) →{0,1,2,3,...,2q1} satisfying f is 1-1 and the induced map f∗:E(G) → {1,3,5,...,2q - 1} defined by f∗(uv) ={f(u)+f(v)/2 if f(u)+f(v)is even f(u)+f(v)+1/2 f(u)+f(v) is odd is a bijection. A graph that admits odd mean labeling is called an odd mean graph. In this paper, we prove that TôCn(n > 3,n≠6)and ToCn(n > 3, n≠ 6), where T is a Tp-tree, are odd mean graphs. © 2018 Utilitas Mathematica Publishing Inc. All rights reserved.