Odd mean labeling of some trees

Abstract

Let G(V, E) be a graph with p vertices and q edges. A graph G is said to be odd mean if there exists a function f: V(G)→{0,1,2,3, ...,2q - 1} satisfying / is 1-1 and the induced map f∗:E(G)→{ 1,3,5, - 1} defined by f∗ (uv)={f(u)+f(v)/2f(u)+f(v)+1/2 if /(u)+/(v) is even if /(u)+/(v) is a bijection- A graPh - if /(u)+/(v) is odd 2 that admits odd mean labeling is called an odd mean graph. In this paper, we prove that Tp-Tree T, T@Pn , T@2P_n ,and (TõK_1,n) ,where T is a Tp-Tree, are odd mean graphs. © 2018 Utilitas Mathematica Publishing Inc. All rights reserved.