Abstract

Let G be a (V,E) graph. G is said to be Square, Cube and Quad difference labeling if there exist a bijection 𝒇:𝑽 𝑮 → {𝟏, 𝟐, … , 𝒑} such that the induced function 𝒇∗:𝑬(𝑮) → 𝑵 given by𝑓∗ 𝑢𝑣 = 𝑓(𝑢)2 − 𝑓(𝑣)2, 𝑓∗ 𝑢𝑣 = 𝑓(𝑢)3 − 𝑓(𝑣)3 & 𝑓∗ 𝑢𝑣=𝑓(𝑢)4−𝑓(𝑣)4, 𝑢𝑣 ∈ 𝐸(𝐺) respectively are all distinct. In this paper, we investigate that the quad difference labeling and prove that the Jewel graph 𝐽𝑛 admits a square difference, cube difference and quad difference labeling.

Keywords

References

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