Skolem Difference Lucas Mean Labeling for Star Related Graphs

A.Ponmoni; S.Navaneetha Krishnan and A.Nagarajan

doi:https://doi.org/10.14445/22315373/IJMTT-V62P515

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 62 | Number 2 | Year 2018 | Article Id. IJMTT-V62P515 | DOI : https://doi.org/10.14445/22315373/IJMTT-V62P515

Skolem Difference Lucas Mean Labeling for Star Related Graphs

A.Ponmoni, S.Navaneetha Krishnan and A.Nagarajan

Abstract

A graph 𝐺 with 𝑝 vertices and 𝑞 edges is said to have Skolem difference Lucas mean labeling if it is possible to label the vertices 𝑥 ∈ 𝑣 with distinct elements 𝑓(𝑥) from the set 1,2, … , 𝐿𝑝+𝑞 in such a way that the edge 𝑒 = 𝑢𝑣is labelled with 𝑓 𝑢 −𝑓(𝑣) 2 if 𝑓 𝑢 − 𝑓(𝑣) is even and 𝑓 𝑢 −𝑓(𝑣 +1 2 if 𝑓 𝑢 − 𝑓(𝑣) is odd, then the resulting edge labels are distinct and are from 𝐿1 , 𝐿2 , … , 𝐿𝑞 .A graph that admits Skolem difference Lucas mean labelling is called a Skolem difference Lucas mean graph. In this paper, we proved for some star related graphs such as 𝐾1,𝑛 + , 𝐾1,𝑚 ⊘ 𝐾1,𝑛 , 𝐾1,𝑚 ⊙ 2𝑃𝑛 , 𝐵𝑚,𝑛 , < 𝐾1,𝑛 (1) ,𝐾1,𝑛 (2) ,𝐾1,𝑛 (3) , … ,𝐾1,𝑛 (𝑚) > , are Skolem difference Lucas mean graph.

Keywords

Skolem Mean Labeling, Skolem difference Mean Labeling , Skolem difference Lucas Mean Labeling.

References

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Citation :

A.Ponmoni, S.Navaneetha Krishnan and A.Nagarajan, "Skolem Difference Lucas Mean Labeling for Star Related Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 62, no. 2, pp. 104-109, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V62P515