Document Type : Research Paper

Authors

• R. Vasuki
• S. Suganthi
• G. Pooranam

Department of Mathematics, Dr. Sivanthi Aditanar College of Engineering, Tiruchendur-628 215, Tamil Nadu, India

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} defined by

f^*(uv) = (f(u) + f(v))/2 if f(u) + f(v) is even
f^*(uv) = (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. In this paper, we have studied an odd meanness property of the subdivision of the slanting ladder SL_n for all n ≥ 2; C_n Θ K₁ for n ≥ 3; the grid P_m × P_n for m, n ≥ 2; C_m@C_n for m, n ≥ 3 and P_2m Θ nK₁ for all m, n ≥ 1..

Keywords

• labeling
• odd mean labeling
• odd mean graph