Some New Results on Antimagic Labeling
DOI:
https://doi.org/10.26713/cma.v15i5.2861Keywords:
Antimagic labeling, Antimagic graph, Book graph, Graph operations, Splitting graphAbstract
A graph with \(q\) edges is called antimagic if its edges can be labeled with \(1, 2, 3,\ldots, q\) without repetition such that the sums of the labels of the edges incident to each vertex are distinct. In this paper, we study antimagic labeling of one point union of cycle, book graph, path union of \(m\) copies of cycles, \(m\)-splitting of path and \(m\)-splitting of cycle.
Downloads
References
H. U. Afzal, A. Alamer and M. Javaid, Computing antimagic labeling of lattically designed symmetric network, IEEE Access 10 (2022), 32394 – 32405, DOI: 10.1109/ACCESS.2022.3160715.
N. Alon, G. Kaplan, A. Lev, Y. Roditty and R. Yuster, Dense graphs are antimagic, Journal of Graph Theory 47(4) (2004), 297 – 309, DOI: 10.1002/jgt.20027.
M. Baca, O. Phanalasy, J. Ryan and A. Semanicová-Fenovcíková, Antimagic labeling of join graphs, Mathematics in Computer Science 9 (2015), 139 – 143, DOI: 10.1007/s11786-015-0218-0.
C. M. Barasara and P. J. Prajapati, Antimagic labeling for some snake graphs, Proyecciones (Antofagasta, On line) 43(2) (2024), 521 – 537, DOI: 10.22199/issn.0717-6279-6005.
C. M. Barasara and P. J. Prajapati, Antimagic labeling of some degree splitting graphs, Ratio Mathematica 48(2023), 444 – 455, DOI: 10.23755/rm.v48i0.1253.
Y. Cheng, A new class of antimagic Cartesian product graphs, Discrete Mathematics 308(24) (2008), 6441 – 6448, DOI: 10.1016/j.disc.2007.12.032.
J. Clark and D. A. Holton, A First Look at Graph Theory, World Scientific, xiv + 330 pages (1991), DOI: 10.1142/1280.
P. Femina and D. A. Xavier, A study of data encryption standard using graph theory, in: Proceedings of the 2nd International Conference on Science, Technology and Management, University of Delhi, New Delhi, India (27th December, 2015), pp. 1928 – 1938 (2015).
J. A. Gallian, Graph labeling, The Electronics Journal of Combinatorics DS#6(Dynamic survey) (2024), DOI: 10.37236/27.
N. Hartsfield and G. Ringel, Pearls in Graph Theory: A Comprehensive Introduction – Revised and Augmented, Academic Press, Boston, x + 249 pages (1990).
J. Jin and Z. Tu, Graph antimagic labeling: A survey, Discrete Mathematics, Algorithms and Applications 16(01) (2024), 2330002, DOI: 10.1142/S1793830923300023.
A. K. Joseph and J. V. Kureethara, The Cartesian product of wheel graph and path graph is antimagic, Communications in Combinatorics and Optimization 8(4) (2023), 639 – 647, DOI: 10.22049/CCO.2022.27645.1307.
A. Krishnaa, Inner magic and inner antimagic graphs in cryptography, Journal of Discrete Mathematical Sciences and Cryptography 22(6) (2019), 1057 – 1066, DOI: 10.1080/09720529.2019.1675298.
J. Sedlácek, Problem 27, in ˇ Theory of Graphs and its Applications, Proceedings of Symposium Smolenice (1963), 163 – 167.
R. Selvakumar and N. Gupta, Fundamental circuits and cut-sets used in cryptography, Journal of Discrete Mathematical Sciences and Cryptography 15(4-5) (2012), 287 – 301, DOI: 10.1080/09720529.2012.10698381.
N. Sridharan and R. Umarani, Antimagic labeling of graphs, International Journal of Engineering Science, Advanced Computing and Bio-Technology 3(1) (2012), 23 – 41, URL: http://ijesacbt.com/archive/Volume3issue1003.pdf.
S. K. Vaidya and N. B. Vyas, Antimagic labeling in the context of switching of a vertex, Annals of Pure and Applied Mathematics 2(1) (2012), 33 – 39.
S. K. Vaidya and N. B. Vyas, Antimagic labeling of some path and cycle related graphs, Annals of Pure and Applied Mathematics 3(2) (2013), 119 – 128.
T.-M. Wang and C.-C. Hsiao, On anti-magic labeling for graph products, Discrete Mathematics 308(16) (2008), 3624 – 3633, DOI: 10.1016/j.disc.2007.07.027.
T. Wang, M. J. Liu and D. M. Li, A class of antimagic join graphs, Acta Mathematica Sinica, English Series 29 (2013), 1019 – 1026, DOI: 10.1007/s10114-012-1559-0.
Y. Zhang and X. Sun, The antimagicness of the Cartesian product of graphs, Theoretical Computer Science 410(8-10) (2009), 727 – 735, DOI: 10.1016/j.tcs.2008.10.023.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an 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 website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.