Odd Harmonious Labeling of Pn ⊵ C4 and  Pn ⊵ D2(C4)

Sabrina Shena Sarasvati, Ikhsanul Halikin, Kristiana Wijaya

Abstract


A graph G with q edges is said to be odd harmonious if there exists an injection f:V(G) → ℤ2q so that the induced function f*:E(G)→ {1,3,...,2q-1} defined by f*(uv)=f(u)+f(v) is a bijection.

Here we show that graphs constructed by edge comb product of path Pn and cycle on four vertices C4 or shadow of cycle of order four D2(C4) are odd harmonious.


Keywords


Odd harmonious labeling; edge comb product; path; cycle; shadow graph.

Full Text:

PDF

DOI: http://dx.doi.org/10.19184/ijc.2021.5.2.5

References

M.E. Abdel-Aal and M.A. Seoud, Futher results on odd harmonious graphs, Int. J. Appl. Graph Theory  Wirel. Ad hoc Netw. Sens. Netw. (GRAPH-HOC), 8(3-4), (2016), 1--14, https://doi.org/10.5121/jgraphoc.2016.8401

M. E. Abdel-Aal, Odd harmonious labelings of cyclic snakes, Int. J. Appl. Graph Theory  Wirel. Ad hoc Netw. Sens. Netw. (GRAPH-HOC), 5(3), (2013), 1--11, https://doi.org/10.5121/jgraphoc.2013.5301

F. Alyani, F. Firmansah, W. Giyarti, and K.A. Sugeng, The odd harmonious labeling of kCn-snake graphs for spesific values of n, that is, for n = 4 and n = 8, Proc. IICMA 2013, (2013), 225--230.

R.L. Graham and N.J.A. Sloane, On additive bases and harmonious graphs, SIAM J. Alg. Disc. Meth. 1(4), (1980), 382--404, https://doi.org/10.1137/0601045

P. Jeyanthi, S. Philo, and M.K. Siddiqui, Odd harmonious labeling of super subdivision graphs, Proyecciones J. Math. 38(1), (2019), 1--11, https://doi.org/10.4067/S0716-09172019000100001

P. Jeyanthi, S. Philo, and M. Youssef, Odd harmonious labeling of grid graph, Proyecciones J. Math. 38 (2019), 411--428, https://doi.org/10.22199/issn.0717-6279-2019-03-0027

P. Jeyanthi and S. Philo, Odd harmonious labeling of certain graphs, J. Appl. Sci. Comput. 6(4), (2019), 1224--1232.

P. Jeyanthi and S. Philo, Odd harmonious labeling of plus graphs, Bull. Int. Math. Virtual Inst. 7 (2017), 515--526, DOI : 10.7251/BIMVI1703515J

P. Jeyanthi and S. Philo, Odd harmonious labeling of some cycle related graphs, Proyecciones J. Math. 35(1), (2016), 85--98, https://doi.org/10.4067/S0716-09172016000100006 

P. Jeyanthi and S. Philo, Odd harmonious labeling of some new families of graphs, Electron. Notes Discrete Math. 48 (2015), 165 --168, https://doi.org/10.1016/j.endm.2015.05.024

P. Jeyanthi, S. Philo, and K.A. Sugeng, Odd harmonious labeling of some new families of graphs, SUT J.  Math. 51(2), (2015), 181--193.

Z. Liang and Z. Bai, On the odd harmonious graphs with applications, J. Appl. Math. Comput. 29 (2009), 105--116, https://doi.org/10.1007/s12190-008-0101-0

D.A. Pujiwati, I. Halikin, and K. Wijaya, Odd harmonious labeling of two graphs containing star, AIP Conf. Proc. 2326, 020019 (2021), https://doi.org/10.1063/5.0039644

G.A. Saputri, K.A. Sugeng, and D. Froncek, The odd harmonious labeling of dumbbell and generalized prims graphs, AKCE Int. J. Graphs Comb. 10(2), (2013), 221--228, https://doi.org/10.1080/09728600.2013.12088738

V. Srividya and R. Govindarajan, On odd harmonious labelling of even cycles with parallel chords and dragons with parallel chords, Int. J. Comput. Aided Eng. Technol.  13(4), (2020), https://doi.org/10.1504/IJCAET.2020.110475

K.A. Sugeng, S. Surip, and R. Rismayati, On odd harmonious labeling of m-shadow of cycle, gear with pendant and shuriken graphs, AIP Conf. Proc.  2192 , 040015 (2019), https://doi.org/10.1063/1.5139141

S.K. Vaidya and N.H. Shah, Some new odd harmonious graphs, Int. J. Math. Soft Comput. 1(1), (2011), 9--16.

S.K. Vaidya and N.H. Shah, Odd harmonious labeling of some graphs, Int. J. Math. Combin. 3 (2012), 105--112, https://doi.org/10.5281/ZENODO.9410


Refbacks

  • There are currently no refbacks.


ISSN: 2541-2205

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

View IJC Stats