THE HARMONIOUS, ODD HARMONIOUS, AND EVEN HARMONIOUS LABELING
Abstract
Suppose is a simple and connected graph with edges. A harmonious labeling on a graph is an injective function so that there exists a bijective function where for each An odd harmonious labeling on a graph is an injective function from to non-negative integer set less than so that there is a function where for every An even harmonious labeling on a graph is an injective function so that there is a bijective function where for each . In this paper, we discuss how to build new labeling (harmonious, odd harmonious, even harmonious) based on the existing labeling (harmonious, odd harmonious, even harmonious)
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References
J. A. Gallian, “A Dynamic Survey of Graph Labeling,” 2017.
R. L. Graham and N. J. A. Sloane, “On Additive Bases and Harmonious Graphs,” SIAM Journal on Algebraic Discrete Methods, vol. 1, no. 4, pp. 382–404, Dec. 1980, doi: 10.1137/0601045.
Z.-H. Liang and Z.-L. Bai, “On the odd harmonious graphs with aplications,” J. Appl.Math. Comput, vol. 29, pp. 105–116, 2009.
M. Bača and M. Z. Youssef, “On harmonious labeling of corona graphs,” Journal of Applied Mathematics, vol. 2014, 2014, doi: 10.1155/2014/627248.
P. Jeyanthi and S. Philo, “Odd Harmonious Labeling of Some New Families of Graphs,” Electronic Notes in Discrete Mathematics, vol. 48, pp. 165–168, Jul. 2015, doi: 10.1016/j.endm.2015.05.024.
D. A. Pujiwati, I. Halikin, and K. Wijaya, “Odd harmonious labeling of two graphs containing star,” in AIP Conference Proceedings, Feb. 2021, vol. 2326. doi: 10.1063/5.0039644.
G. A. Saputri, K. A. Sugeng, and D. Froncek, “The Odd Harmonious Labeling of Dumbbell and Generalized Prism Graphs,” AKCE International Journal of Graphs and Combinatorics, vol. 10, no. 2, pp. 221–228, 2013, doi: 10.1080/09728600.2013.12088738.
S. S. Sarasvati, I. Halikin, and K. Wijaya, “Odd Harmonious Labeling of P_n⊵C_4 and P_n⊵D_2 (C_4 ),” Indonesian Journal of Combinatorics, vol. 5, no. 2, p. 94, Dec. 2021, doi: 10.19184/ijc.2021.5.2.5.
K. A. Sugeng, S. Surip, and R. Rismayati, “On odd labeling of m-shadow of cycle, gear with pendant and Shuriken graphs,” in AIP Conference Proceedings, Dec. 2019, vol. 2192. doi: 10.1063/1.5139141.
S. K. Vaidya and N. H. Shah, “Odd Harmonious Labeling of Some Graphs,” 2012.
P. B. Sarasija and R. Binthiya, “Even Harmonious Graphs with Applications,” Internat. J. Comput. Sci. Infor. Security, vol. 9, pp. 161–163, 2011.
J. A. Gallian, L. A. Schoenhard, and S. Arumugam, “Even Harmonious Graphs,” AKCE International Journal of Graphs and Combinatorics, vol. 11, no. 1, pp. 27–49, 2014, doi: 10.1080/09728600.2014.12088761.
J. A. Gallian and D. Stewart, “Even harmonious labelings of disjoint unions with even sequential graphs,” J. Graph Labeling, vol. 1, no. 1, pp. 1–10, 2015.
J. A. Gallian and D. Stewart, “Even harmonious labelings of disjoint graphs with a small component,” AKCE J. Graphs Combin, vol. 12, no. 2–3, pp. 204–215, 2015.
J. A. Gallian and D. Stewart, “Properly even harmonious labelings of disconnected graphs,” AKCE International Journal of Graphs and Combinatorics, vol. 12, no. 2–3, pp. 193–203, Nov. 2015, doi: 10.1016/j.akcej.2015.11.015.
G. Chartrand and P. Zhang, A first course in graph theory. Dover Publications, 2012.
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