PMC-LABELING OF SOME CLASSES OF GRAPHS CONTAINING CYCLES
Abstract
Let be a graph with p vertices and q edges. We have introduced a new graph labeling method using integers and cordial-related works and investigated some graphs for this labeling technique. Using this labeling concept, we have examined the graphs like path, cycle, star, complete graph, comb, and wheel graph. The first research paper on graph theory was published by Leonhard Euler. However, he did not use the word ‘graph’ in his work. In the early stages of the development of the subject, the vertices of a graph were specified as , and the edges were denoted by, . In recent times, several researchers have attempted to provide different types of labeling to the vertices and edges of a graph by identifying the relevant mathematical properties. The present paper provides a novel method of labeling by employing integers, which may form a foundation for future research work. In this paper, we investigate the pair mean cordial labeling behavior of some cycle-related graphs like the ice cream graph, closed web graph, circulant graph, zig-zag chord graph, pentagonal circular ladder, djembe graph, quadrilateral friendship graph, and origami graph.
Downloads
References
A. Rosa, “ON CERTAIN VALUATIONS OF THE VERTICES OF A GRAPH,” Theory of Graphs (Internat. Symposium, Rome, July 1966), pp. 349–355, 1967.
F. Harary, GRAPH THEORY. New Delhi: Narosa Publishing House, 1988.
A. Gallian, “A DYNAMIC SURVEY OF GRAPH LABELING,” Electron J Comb, vol. 26, 2023.
I. Cahit, “CORDIAL GRAPHS: A WEAKER VERSION OF GRACEFUL AND HARMONIOUS GRAPHS,” Ars comb., vol. 23, pp. 201–207, 1987.
A. Lasim, I. Halikin, and K. Wijaya, “THE HARMONIOUS, ODD HARMONIOUS, AND EVEN HARMONIOUS LABELING,” BAREKENG: Jurnal Ilmu Matematika dan Terapan, vol. 16, no. 4, pp. 1131–1138, Dec. 2022, doi: 10.30598/barekengvol16iss4pp1131-1138.
N. Inayah, A. Erfanian, and M. Korivand, “TOTAL PRODUCT AND TOTAL EDGE PRODUCT CORDIAL LABELINGS OF DRAGONFLY GRAPH (Dg n ),” Journal of Mathematics, vol. 2022, no. 1, Jan. 2022, doi: 10.1155/2022/3728344.
A. Petrano and R. Rulete, “ON TOTAL PRODUCT CORDIAL LABELING OF SOME GRAPHS,” Internat. J. Math. Appl., vol. 5, no. 2B, pp. 273–284, 2017.
U. M. Prajapati and S. J. Gajjar, “PRIME CORDIAL LABELING OF GENERALIZED PRISM GRAPH Y_(m,n),” Ultra Scientist, vol. 27, no. 3, pp. 189–204, 2015.
N. B. Rathod and K. K. Kanani, “$k$-CORDIAL LABELING OF TRIANGULAR BELT, ALTERNATE TRIANGULAR BELT, BRAID GRAPH and $Z$-$P_n$,” Int. J. Math. And Appl, vol. 5, no. 4, pp. 655–662, Dec. 2017.
L. A. Zalzabila, D. Indriati, and S. T. Martini, “EDGE IRREGULAR REFLEXIVE LABELING ON ALTERNATE TRIANGULAR SNAKE AND DOUBLE ALTERNATE QUADRILATERAL SNAKE,” BAREKENG: Journal of Mathematics and Its Application, vol. 17, no. 4, pp. 1941–1948, 2023.
P. Sumathi and S. Kavitha, “QUOTIENT 4-CORDIAL LABELING OF SOME LADDER GRAPHS,” J Algebr Stat, vol. 13, no. 2, pp. 3243–3264, 2022.
M. A. Seoud and H. F. Helmi, “ON PRODUCT CORDIAL GRAPHS,” Ars Combin., vol. 101, pp. 519–529, 2011.
V. P. Swetha and R. Vanithasree, “A STUDY ON COMBINATION OF SHELL GRAPH AND PATH P_2 GRAPH,” JETIR, vol. 6, no. 5, pp. 578–580, 2019.
S. N. Daoud and A. N. Elsawy, “EDGE EVEN GRACEFUL LABELLING OF NEW FAMILIES OF GRAPHS,” Journal of Taibah University for Science, vol. 13, no. 1, pp. 579–591, Dec. 2019, doi: 10.1080/16583655.2019.1611180.
V. S. Philomena and S. Vasavi, “SQUARE DIFFERENCE AND CUBE DIFFERENCE LABELLING OF EXTENDED KUSUDAMA FLOWER GRAPH,” Advances and Applications in Mathematical Sciences, vol. 22, no. 7, pp. 1603–1611, 2023.
R. Ponraj and S. Prabhu, “PAIR MEAN CORDIAL LABELING OF GRAPHS,” Journal of Algorithms and Computation, vol. 54, no. 1, pp. 1–10, 2022, [Online]. Available: http://jac.ut.ac.ir
R. Ponraj and S. Prabhu, “ON PAIR MEAN CORDIAL GRAPHS,” J. Appl. & Pure Math, vol. 5, no. 4, pp. 237–253, 2023, doi: 10.23091/japm.2023.237.
R. Ponraj and S. Prabhu, “PAIR MEAN CORDIAL LABELING OF HEXAGONAL SNAKE, IRREGULAR QUADRILATERAL SNAKE AND TRIPLE TRIANGULAR SNAKE,” Indian Journal of Natural Sciences, vol. 15, no. 83, pp. 73075–73081, 2024.
R. Ponraj and S. Prabhu, “PAIR MEAN CORDIAL LABELING OF HURDLE, KEY, LOTUS, AND NECKLACE GRAPHS,” BAREKENG: Jurnal Ilmu Matematika dan Terapan, vol. 18, no. 4, pp. 2795–2804, Oct. 2024, doi: 10.30598/barekengvol18iss4pp2795-2804.
U. M. Prajapati and N. B. Patel, “EDGE PRODUCT CORDIAL LABELING OF SOME CYCLE RELATED GRAPHS,” Open Journal of Discrete Mathematics, vol. 06, no. 04, pp. 268–278, 2016, doi: 10.4236/ojdm.2016.64023.
Copyright (c) 2025 R Ponraj, S Prabhu, M Sivakumar
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Authors who publish with this Journal agree to the following terms:
- Author retain copyright and grant the journal right of first publication with the work simultaneously licensed under a creative commons attribution license that allow others to share the work within an acknowledgement of the work’s authorship and initial publication of this journal.
- Authors are able to enter into separate, additional contractual arrangement for the non-exclusive distribution of the journal’s published version of the work (e.g. acknowledgement of its initial publication in this journal).
- Authors are permitted and encouraged to post their work online (e.g. in institutional repositories or on their websites) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published works.
1.gif)
