Open Access   Article Go Back

Odd Harmonious Labeling of Subdivided Shell Graphs

P.Jeyanthi 1 , S. Philo2

Section:Research Paper, Product Type: Journal Paper
Volume-07 , Issue-05 , Page no. 77-80, Mar-2019

CrossRef-DOI:   https://doi.org/10.26438/ijcse/v7si5.7780

Online published on Mar 10, 2019

Copyright © P.Jeyanthi, S. Philo . 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.

View this paper at   Google Scholar | DPI Digital Library

XML View
PDF Download

How to Cite this Paper

  • IEEE Citation
  • MLA Citation
  • APA Citation
  • BibTex Citation
  • RIS Citation

IEEE Style Citation: P.Jeyanthi, S. Philo, “Odd Harmonious Labeling of Subdivided Shell Graphs,” International Journal of Computer Sciences and Engineering, Vol.07, Issue.05, pp.77-80, 2019.

MLA Style Citation: P.Jeyanthi, S. Philo "Odd Harmonious Labeling of Subdivided Shell Graphs." International Journal of Computer Sciences and Engineering 07.05 (2019): 77-80.

APA Style Citation: P.Jeyanthi, S. Philo, (2019). Odd Harmonious Labeling of Subdivided Shell Graphs. International Journal of Computer Sciences and Engineering, 07(05), 77-80.

BibTex Style Citation:
@article{Philo_2019,
author = {P.Jeyanthi, S. Philo},
title = {Odd Harmonious Labeling of Subdivided Shell Graphs},
journal = {International Journal of Computer Sciences and Engineering},
issue_date = {3 2019},
volume = {07},
Issue = {05},
month = {3},
year = {2019},
issn = {2347-2693},
pages = {77-80},
url = {https://www.ijcseonline.org/full_spl_paper_view.php?paper_id=809},
doi = {https://doi.org/10.26438/ijcse/v7i5.7780}
publisher = {IJCSE, Indore, INDIA},
}

RIS Style Citation:
TY - JOUR
DO = {https://doi.org/10.26438/ijcse/v7i5.7780}
UR - https://www.ijcseonline.org/full_spl_paper_view.php?paper_id=809
TI - Odd Harmonious Labeling of Subdivided Shell Graphs
T2 - International Journal of Computer Sciences and Engineering
AU - P.Jeyanthi, S. Philo
PY - 2019
DA - 2019/03/10
PB - IJCSE, Indore, INDIA
SP - 77-80
IS - 05
VL - 07
SN - 2347-2693
ER -

           

Abstract

A graph G(p, q) is said to be odd harmonious if there exists an injection f: V(G) → {0, 1, 2, …, 2q-1} such that the induced function f*:E(G)→{1,3,...,2q−1} defined by f * (uv) = f(u) + f(v) is a bijection. In this paper we prove that the subdivided shell graph, disjoint union of two subdivided shell graph, subdivided shell flower graph and subdivided uniform shell bow graph are odd harmonious.

Key-Words / Index Term

disjoint union of graph, harmonious labeling, subdivided shell graph, odd harmonious labeling

References

[1] Deb P. and Limaye N.B., “On Harmonious Labeling of Some Cycle Related Graphs”, Ars Combina.,65(2002), 177-197.
[2] Jeba Jesintha J and Ezhilarasi Hilda K., “Subdivided Uniform Shell Bow Graphs are one Modulo three Graceful”, Mathematical Sciences International Research Journal, Vol.3, No.2(2014),645-646.
[3] Jeba Jesintha J and Ezhiarasi Hilda K.,Variation of “Graceful Labeling on Disjoint Union of two Subdivided Shell Graphs”, Annals of Pure and Applied Mathematics, Vol.8, No.2(2014), 19-25.
[4] Graham R. L. and Sloane N.J.A, “On Additive bases and Harmonious Graphs”, SIAM J. Algebr. Disc. Meth., 4(1980), 382–404.
[5] Harary F., “Graph Theory”, Addison-Wesley, Massachusetts, 1972.
[6] Liang Z., Bai Z., “On the Odd Harmonious Graphs with Applications”, J.Appl. Math.Comput., 29 (2009), 105–116.
[7] Jeyanthi P., Philo S. and Kiki A.Sugeng, “Odd Harmonious Labeling of Some New Families of Graph”s, SUT Journal of Mathematics,Vol.51, No.2(2015), 53-65.
[8] Jeyanthi P., Philo S., “Odd Harmonious Labeling of Some Cycle Related Graphs”, Proyecciones Journal of Mathematics, Vol.35, No.1, (2016)85-98.
[9] Jeyanthi P., Philo S, “Odd harmonious Labeling of Plus Graphs”, Bulletin of the International Mathematical Virtual Institute,Vol.7(2017),515-526.
[10] Jeyanthi P., Philo S., Siddiqui M.K., “Odd Harmonious Labeling of Super Subdivision Graphs”, Proyecciones Journal of Mathematics, Vol.38 No.1(2019), to appear.
[11]Jeyanthi P., Philo S., Maged Z Youssef., “Odd harmonious Labeling of Grid Graphs”, Proyecciones Journal of Mathematics, to appear.
[12]Jeyanthi P., Philo S., “Odd Harmonious Labeling of Some New Graphs”, Southeast Asian Bulletin of Mathematics, to appear.
[13]Jeyanthi P., Philo S., “Odd Harmonious Labeling of Step Ladder Graphs”, Utilitas Mathematica, to appear.