Further results on odd mean labeling of some subdivision graphs

Document Type: Research Paper

Authors

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 SLn for all n ≥ 2; Cn  Θ K1 for n ≥ 3; the grid P× Pn for m, n ≥ 2; Cm@Cn for m, n ≥ 3 and P2Θ nK1 for all m, n ≥ 1..

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