k-ZUMKELLER LABELING OF CERTAIN GRAPHS

Abstract

Let G be any graph. Then a one-one function 𝑓: 𝑉 → ℕ is said to be a k-Zumkeller labeling of G if the induced function 𝑓 ∗ : 𝐸 → ℕ defined by 𝑓 ∗ (𝑥𝑦) = 𝑓(𝑥)𝑓(𝑦) satisfies the following conditions: (i) For every 𝑥𝑦 ∈ 𝐸, 𝑓 ∗ (𝑥𝑦) is a Zumkeller number. (ii) |𝑓 ∗ (𝐸)| = 𝑘, where |𝑓 ∗ (𝐸)| denotes the number of distinct Zumkeller numbers on the edges of G. In this paper, we prove the existence of k-Zumkeller labeling for certain graphs like tadpole, banana, friendship, and firecracker graphs.

Keywords

• zumkeller number
• banana graph
• friendship graph
• firecracker graph
• tadpole graph