A PROPERLY EVEN HARMONIOUS LABELING OF SOME WHEEL GRAPH W_n FOR n IS EVEN
Abstract
A properly even harmonious labeling of a graph G with q edges is an injective mapping f from the vertices of graph G to the integers from 0 to 2q-1 such that induces a bijective mapping f* from the edges of G to {0,2,...,2q-2} defined by f*(v_iv_j)=(f(v_i)+f(v_j))(mod2q). A graph that has a properly even harmonious labeling is called a properly even harmonious graph. In this research, we will show the existence of a properly even harmonious labeling of some wheel graph W_n for n is even.
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References
Slamin, Teori Graf dan Aplikasinya. Malang: Dream Litera Buana, 2019.
J. Akiyama and M. Kano, Factors and Factorizations of Graphs: Proof Techniques in Factor Theory. Berlin: Springer Berlin Heidelberg, 2011.
G. Chartrand and P. Zhang, “A First Course in Graph Theory - Chartrand, Zhang (Dover Publications, 2012, 9780486483689, eng).” 2012.
J. Harris, J. L. Hirst, and M. Mossinghoff, Combinatorics and Graph Theory, 2nd Edition. New York: Springer, 2008.
R. G. Bartle and D. R. Sherbert, Introduction to Real Analysis, 4th Edition. USA: John Wiley&Sons Inc., 2011.
W. D. Wallis and A. Marr, Magic Graphs, 2nd Edition. Boston: Birkhauser, 2013.
R. L. Graham and N. J. A. Sloane, “On Additive Bases and Harmonious Graphs,” SIAM J. Algebr. Discret. Methods, vol. 1, no. 4, pp. 382–404, 1980, doi: 10.1137/0601045.
Z. H. Liang and Z. L. Bai, “On the Odd Harmonious Graphs with Applications,” J. Appl. Math. Comput., vol. 29, pp. 105–116, 2009.
P. Sarasija and R. Binthiya, “Even Harmonious Graphs with Applications,” Int. J. Comput. Sci. Inf. Secur. IJCSIS, vol. 9, no. 6, p. 355, 2011, [Online]. Available: http://sites.google.com/site/ijcsis/
J. A. Gallian, “A Dynamic Survey of Graph Labeling,” Electron. J. Comb., no. March, pp. 1–219, 2017, doi: 10.37236/11668.
A. Lasim, I. Halikin, and K. Wijaya, “The Harmonious, Odd Harmonious, and Even Harmonious Labeling,” BAREKENG J. Ilmu Mat. dan Terap., vol. 16, no. 4, pp. 1131–1138, 2022, doi: 10.30598/barekengvol16iss4pp1131-1138.
J. A. Gallian and D. Stewart, “Properly Even Harmonious Labelings of Disconnected Graphs,” AKCE Int. J. Graphs Comb., vol. 12, no. 2–3, pp. 193–203, 2015, doi: 10.1016/j.akcej.2015.11.015.
Y. Ulfa and P. Purwanto, “Properly Even Harmonious Labelings of Complete Tripartite Graph K 1, mn and Union of Two Coconut Tree Graphs,” AIP Conf. Proc., vol. 2330, no. March, 2021, doi: 10.1063/5.0043182.
M. K. Setiono, “Pelabelan Harmonis Genap Sejati pada Graf Petersen Diperumum,” Universitas Islam Negeri Maulana Malik Ibrahim, 2021.
J. A. Gallian and L. A. Schoenhard, “Even Harmonious Graphs,” AKCE Int. J. Graphs Comb., vol. 11, no. 1, pp. 27–49, 2014, doi: 10.1080/09728600.2014.12088761.
O. Mbianda, “Properly Even Harmonious Graphs [Thesis],” US Fac. Grad. Sch. Univ. Minnesota, 2016.
D. Taqiyah and B. Rahadjeng, “Pelabelan Harmonis Genap Sejati dari Beberapa Graf Terhubung,” J. Ilm. Mat., vol. 10, no. 0, 2022.
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