Near Skolem Difference Mean Labeling of
Special Types of Trees

S. ShenbagaDevi; A. Nagarajan

doi:https://doi.org/10.14445/22315373/IJMTT-V52P568

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 52 | Number 7 | Year 2017 | Article Id. IJMTT-V52P568 | DOI : https://doi.org/10.14445/22315373/IJMTT-V52P568

Near Skolem Difference Mean Labeling of Special Types of Trees

S. ShenbagaDevi, A. Nagarajan

Citation :

S. ShenbagaDevi, A. Nagarajan, "Near Skolem Difference Mean Labeling of Special Types of Trees," International Journal of Mathematics Trends and Technology (IJMTT), vol. 52, no. 7, pp. 474-478, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V52P568

Abstract

Let 𝐺 be a 𝑝, 𝑞 graph and 𝑓: 𝑉(𝐺) → {1,2, … , 𝑝 + 𝑞 − 1, 𝑝 + 𝑞 +2} be an injection. For each edge 𝑒 = 𝑢𝑣, the induced edge labeling 𝑓 ∗ is defined as follows: 𝑓 ∗ 𝑒 = 𝑓 𝑢 − 𝑓(𝑣) 2 𝑖𝑓 𝑓 𝑢 − 𝑓 𝑣 𝑖𝑠 𝑒𝑣𝑒𝑛 𝑓 𝑢 −𝑓(𝑣) + 1 2 𝑖𝑓 𝑓 𝑢 − 𝑓 𝑣 𝑖𝑠 𝑜𝑑𝑑 Then 𝑓 is called Near Skolem difference mean labeling if 𝑓 ∗ (𝑒) are all distinct and from 1,2,3, … . 𝑞 . A graph that admits a Near Skolem difference mean labeling is called a Near Skolem difference mean graph. In this paper, we investigate near Skolem difference mean labelling of some special types of trees like the banana tree, the coconut tree, the 𝐻 − graph, the lily graph, the jelly fish graph and the graph T 𝐾1,𝑛1 ◦𝐾1,𝑛2 ◦◦◦𝐾1,𝑛𝑚

Keywords

Near Skolem difference mean labeling, Near Skolem difference mean graphs.

References

[1] F. Harary(2001), Graph Theory, Narosa Publishing House, New Delhi.
[2] J. A.Gallian(2008), A Dynamic Survey of Graph Labeling, The Electronic Journal of Combinatorics, 15, #DS6.
[3] K. Murugan and A. Subramanian (2011)., Skolem difference mean labelling of H-graphs, International Journal of Mathematics and Soft Computing, Vol.1, No. 1, pp. 115-129.
[4] S. Shenbaga Devi and A. Nagarajan, On Near Skolem Difference Mean Graphs (Communicated).