Volume 71 | Issue 4 | Year 2025 | Article Id. IJMTT-V71I4P102 | DOI : https://doi.org/10.14445/22315373/IJMTT-V71I4P102
Received | Revised | Accepted | Published |
---|---|---|---|
25 Feb 2025 | 28 Mar 2025 | 14 Apr 2025 | 29 May 2025 |
A sum divisor cordial labeling of a graph G with vertex set V(G) is a bijection f from V(G) to {1, 2, 3,…, |V(G)|} such that an edge u v is assigned the label 0 if 2 divides f(u)+f(v) and 1 otherwise; and it Satisfies the condition |e f (0) – e f (1) | ≤ 1, then a graph with a sum divisor cordial labeling is called a sum divisor cordial graph. In this paper, we apply the sum divisor cordial labeling of path union and a cycle of zero divisor graphs. We proved that the path union and cycle of zero divisor graphs are sum divisor cordial.
Cordial graphs, Cycle of graphs, path union, Sum divisor cordial labeling, Sum divisor cordial graphs, Zero divisor graphs.
[1] Alexander Rosa, “On Certain Valuations of the Vertices of a Graph, Theory of Graphs,” Gordon and Breach, N.Y. and Paris, pp. 349
355, 1967.
[Google Scholar]
[2] Roberto Frucht, and Frank Harary, “On the Corona of Two Graphs,” Aequationes Math, vol. 4, pp. 322-325, 1970.
[CrossRef] [Google Scholar] [Publisher Link]
[3] Istvan Beck, “Coloring of Commutative Rings,” Journal of Algebra, vol. 116, no. 1, pp. 208-226, 1988.
[CrossRef] [Google Scholar] [Publisher Link]
[4] R. Varatharajan, S. Navanaeetha Krishnan, and K. Nagarajan, Divisor Cordial Graphs, International Journal of Mathematical
Combinatorics, vol. 4, pp. 15-25, 2011.
[Google Scholar] [Publisher Link]
[5] S.K. Vaidya, and N.H Shah, “Further Results on Divisor Cordial Labeling,” Annals of Pure and Applied Mathematics, vol. 4, no. 2, pp.
150-159, 2013.
[Google Scholar] [Publisher Link]
[6] Joseph A. Gallian, “A Dynamic Survey of Graph Labeling,” The Electronic Journal of Combinatorics, vol. 18, 2018.
[Google Scholar] [Publisher Link]
[7] A. Lourdusamy, and F. Patrick, “Sum Divisor Cordial Labeling for Star and Ladder Related Graphs,” Proyecciones Journal of
Mathematics, vol. 35, no. 4, pp. 437-455, 2016.
[CrossRef] [Google Scholar] [Publisher Link]
[8] T. Tamizh Chelvam, and C. Subramanian, “Sum Cordial Labeling of Zero-Divisor Graphs,” International Journal of Mathematical
Archive, vol. 9, no. 2, pp. 146-151, 2018.
[Google Scholar]
[9] E. Veronisha A. Lourdusamy, and F. Joy Beaula, “Total 3-sum Cordial Labeling on Zero Divisor Graphs,” AIP Conference
Proceedings, vol. 2764, no. 1, 2023.
[CrossRef] [Google Scholar] [Publisher Link]
[10] V. Jude Annie Cynthia, and E. Padmavathy, “Signed and Signed Product Cordial Labeling of Cylinder Graphs and Banana Tree,”
International journal of Mathematics Trends and Technology, vol. 65, no 3, pp. 36-43, 2019.
[CrossRef] [Google Scholar] [Publisher Link]
[11] V. J. Kaneria, and Meera Meghpara2, “Mean Labeling for Some Cycle of Graphs,” International Journal of Mathematical sciences and
Engineering Applications, vol. 9, no. 2, pp. 267-274, 2015.
[Publisher Link]
[12] Shaik Sajana, K.K. Srimitra, and D. Bharathi, “Intersection of Graph of Zero Divisors of the Ring Zn,” Journal of AIP Conference
Proceedings, vol. 2246, no. 1, 2020.
[CrossRef] [Google Scholar] [Publisher Link]
[13] V.J. Kaneria, H.M. Makadia, and M.M. Jariya, “Graceful labeling for cycle of Graphs,” International Journal of Mathematics Research,
vol. 6, no. 2, pp. 173-178, 2014.
[Publisher Link]
M. Lakshmi, D. Bharathi, "SDC Labeling on Path Union and Cycle of Zero Divisor Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 71, no. 4, pp. 8-20, 2025. Crossref, https://doi.org/10.14445/22315373/IJMTT-V71I4P102