Difference Labelling of Jewel Graph

V.Govindan; S.Dhivya

doi:https://doi.org/10.14445/22315373/IJMTT-V65I4P512

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 65 | Issue 4 | Year 2019 | Article Id. IJMTT-V65I4P512 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I4P512

Difference Labelling of Jewel Graph

V.Govindan, S.Dhivya

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

Square difference, Cube difference, Quad difference, Jewel graph, Difference labeling.

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Citation :

V.Govindan, S.Dhivya, "Difference Labelling of Jewel Graph," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 4, pp. 64-68, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I4P512