Harmonious and Pell Labeling for Some Extended Duplicate Graph

R. Avudainayaki¹ , B. Selvam²

Section:Research Paper, Product Type: Isroset-Journal
Vol.5 , Issue.6 , pp.152-156, Dec-2018

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.152156

Online published on Dec 31, 2018

Copyright © R. Avudainayaki, B. Selvam . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
A Graph G is said to be harmonious if there exist an injection f : V(G)→ Zq such that the induced function f *: E(G)→ Zq defined by f *(uv) = (f(u) + f(v)) (mod q) is a bijection. Let G be a (p, q) graph. If there exists a mapping f: V(G) →{ 0,1, …., p-1} such that the induced function f* : E(G) → N given by f*(uv) = f(u) +2 f(v) for every uv E(G) are all distinct where u,v ≥ 0, then the function f is called a Pell labeling. In this paper, we proved that the extended duplicate graph of arrow graph and splitting graph of path admits harmonious and pell labeling.

Key-Words / Index Term :
Arrow graph, Splitting graph of path, Duplicate graph, Harmonious , Pell labeling

References :
[1] Gallian J.A, “A Dynamic Survey of graph labeling”, the Electronic Journal of combinatories, 19, # DS6 (2015).Pp. 189-198.
[2] R. L. Graham and N.J.A. Sloane, on additive bases and harmonious graphs, SIAM, J. Alg. Disc. Meth. 1, (1980), 382 – 404.
[3] Rosa A, On certain Valuations of the vertices of a graph, Theory of graphs (Internat. Symposium, Rome, July 1966), Gordon and Breech, N.Y. and Dunod paris, 1967.pp. 349- 355.
[4] E.Sampath kumar, “On duplicate graphs”, Journal of the Indian Math. Soc. 37 (1973), 285 – 293.
[5] J.Shiama, Pell labeling for some graphs, Asian Journal of Current Engineering and Maths, 2(4) (2013).
[6] Thirusangu,K, Selvam.B. and Ulaganathan.P.P, Cordial labelings in extended duplicate twig graphs ,International Journal of computer, mathematical sciences and applications, Vol.4, Nos 3-4, (2010), pp.319-328.