Further Results On Odd Mean Graphs

Abstract

Let G = (V,E) be a graph with p vertices and q edges. A graph G is said to have an odd mean labeling if there exists a function f : V (G)→ {0, 1, 2, . . . , 2q − 1} 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 if f(u) + f(v) is odd. is a bijection. A graph that admits an odd mean labeling is called an odd mean graph. Here we study about the odd mean behaviour of some standard graphs.