On reverse super edge trimagic labeling of path-related graphs and cycle-related graphs

Titin Srimartini; Yeni Susanti; Budi Surodjo; Titin Srimartini; Yeni Susanti; Budi Surodjo

doi:10.3934/math.20261228

AIMS Mathematics

2026, Volume 11, Issue 9: 31041-31061. doi: 10.3934/math.20261228

Previous Article Next Article

Research article

On reverse super edge trimagic labeling of path-related graphs and cycle-related graphs

1.
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Yogyakarta, Indonesia
2.
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Sebelas Maret, Surakarta, Indonesia

Received: 09 July 2026 Revised: 10 September 2026 Accepted: 15 September 2026 Published: 22 September 2026
MSC : 05C76, 05C78

A graph is said to admit a reverse super edge trimagic labeling if its vertices and edges can be bijectively labeled with consecutive integers such that the differences between the edge labels and the sums of the labels of their end vertices attain exactly three distinct values, with the vertex labels occupying the smallest integers. In this paper, we establish new results on the existence of reverse super edge trimagic labelings for several families of path- and cycle-related graphs. Specifically, we prove that path graphs, the $ m $-copy path graphs, corona products of a path and a null graph, cycle graphs, $ m $-copy cycle graphs, and corona products of a cycle and a null graph admit reverse super edge trimagic labelings under specified conditions on their parameters. For each graph family, we provide explicit constructions of the corresponding labelings and determine the associated three magic constants. These results extend the known results on reverse super edge trimagic labelings to broader families of path and cycle-related graphs.
- reverse super edge trimagic labeling,
- path graph,
- cycle graph,
- corona product of a graph
Citation: Titin Srimartini, Yeni Susanti, Budi Surodjo. On reverse super edge trimagic labeling of path-related graphs and cycle-related graphs[J]. AIMS Mathematics, 2026, 11(9): 31041-31061. doi: 10.3934/math.20261228

Related Papers:

Abstract

A graph is said to admit a reverse super edge trimagic labeling if its vertices and edges can be bijectively labeled with consecutive integers such that the differences between the edge labels and the sums of the labels of their end vertices attain exactly three distinct values, with the vertex labels occupying the smallest integers. In this paper, we establish new results on the existence of reverse super edge trimagic labelings for several families of path- and cycle-related graphs. Specifically, we prove that path graphs, the $ m $-copy path graphs, corona products of a path and a null graph, cycle graphs, $ m $-copy cycle graphs, and corona products of a cycle and a null graph admit reverse super edge trimagic labelings under specified conditions on their parameters. For each graph family, we provide explicit constructions of the corresponding labelings and determine the associated three magic constants. These results extend the known results on reverse super edge trimagic labelings to broader families of path and cycle-related graphs.

References

[1]	W. D. Wallis, Magic Graphs, 2 Eds, Basel: Birkhauser, 2013.
[2]	J. A. Gallian, A dynamic survey of graph labeling, Electron. J. Comb., 6 (2023), DS6.
[3]	J. Sedláček, Theory of graphs and its applications, Proc. Symp., 1963,163–164.
[4]	A. Kotzig, A. Rosa, Magic valuations of finite graphs, Canad. Math. Bull., 13 (1970), 451–461. https://doi.org/10.4153/CMB-1970-084-1 doi: 10.4153/CMB-1970-084-1
[5]	J. B. Babujee, On edge bimagic labeling, Int. J. Comb. Inform. Syst. Sci., 28 (2004), 239–244. http://doi.org/10.22457/apam.v13n1a8 doi: 10.22457/apam.v13n1a8
[6]	J. B. Babujee, R. Jagadesh, Superior edge bimagic labeling, Int. J. Math Comb., 1 (2008), 107–116.
[7]	J. B. Babujee, R. Jagadesh, Super edge bimagic labeling for graph with cycles, Pacific-Asian J. Math., 2 (2008), 113–122.
[8]	A. A. Jothi, N. G. David, J. B. Babujee, On edge magic and bimagic labeling of graphs, Int. J. Pure Appl. Math., 101 (2015), 711–718.
[9]	J. B. Babujee, R. Jagadesh, Super edge bimagic labeling for some classes of connected graphs derived from fundamental graphs, Int. J. Comb. Graph Theory Appl., 4 (2019), 119–126.
[10]	S. Subbulakshmi, R. Kokila, Edge bimagic labeling of graphs K2, N, KN, 2, N, Bistar, nC4, and double wheel, J. Phys.: Conf. Ser., 1377 (2019), 012013. http://doi.org/10.1088/1742-6596/1377/1/012013 doi: 10.1088/1742-6596/1377/1/012013
[11]	A. N. Fadhilah, T. S. Martini, Super edge bimagic and super edge trimagic total labeling of hibiscus graph, AIP Conf. Proc., 3285 (2022), 020003. https://doi.org/10.1063/5.0262408 doi: 10.1063/5.0262408
[12]	M. R. Z. El Deen, I. M. Hanafi, S. G. Shehda, N. A. Omar, Super edge bimagic and trimagic total labeling for some graphs, Alfarama J. Basic Appl. Sci.‌, 6 (2025), 431–442. http://doi.org/10.21608/ajbas.2025.403080.1267 doi: 10.21608/ajbas.2025.403080.1267
[13]	C. Jayasekaran, M. Reeges, C. Davidraj, Edge trimagic labeling of some graphs, Int. J. Comb. Graph Theory Appl., 6 (2013), 175–186.
[14]	M. Reeges, C. Jayasekaran, Edge trimagic total labeling of disconnedted graphs, Int. J. Math. Trenda Technol., 6 (2014), 44–53. https://doi.org/10.14445/22315373/IJMTT-V6P504 doi: 10.14445/22315373/IJMTT-V6P504
[15]	M. Reeges, C. Jayasekaran, Super edge trimagic total labeling of generalized prism and web graphs, J. Discrete Math. Sci. Cryptogr., 19 (2016), 81–92. https://doi.org/10.1080/09720529.2015.1101880 doi: 10.1080/09720529.2015.1101880
[16]	C. Jayasekaran, J. L. Flower, On edge trimagic labeling of umbrella, dumb bell and circular ladder graphs, J. Ann. Pure Appl. Math., 13 (2017), 73–87. http://doi.org/10.22457/apam.v13n1a8 doi: 10.22457/apam.v13n1a8
[17]	C. Jayasekaran, J. L. Flower, Edge trimagic total labeling of mobius ladder, book and dragon graphs, J. Ann. Pure Appl. Math., 13 (2017), 151–163. http://doi.org/10.22457/apam.v13n2a1 doi: 10.22457/apam.v13n2a1
[18]	A. J. Nawawi, T. S. Martini, T. A. Kusmayadi, Super edge trimagic total labeling of Dovetail Corona Null Graph $D_n \odot N_m$, AIP Conf. Proc., 3285 (2025), 020006. https://doi.org/10.1063/5.0262388 doi: 10.1063/5.0262388
[19]	N. S. Hungund, D. G. Akka, Reverse super edge-magic strength of some new classes of graphs, J. Discrete Math. Sci. Cryptogr., 16 (2013), 19–29. https://doi.org/10.1080/09720529.2013.778462 doi: 10.1080/09720529.2013.778462
[20]	K. A. Reddy, S. S. Basha, New classes of reverse super edge magic graphs, AIMS Math., 7 (2021), 3590–3602. https://doi.org/10.3934/math.2022198 doi: 10.3934/math.2022198
[21]	S. S. Basha, K. A. Reddy, Reverse edge magic labeling of a cycle with chords, unions of cycles and unions of paths, Adv. Math.: Sci. J., 10 (2021), 571–581. https://doi.org/10.37418/amsj.10.1.56 doi: 10.37418/amsj.10.1.56
[22]	K. Amuthavalli, P. Sugapriya, Reverse super edge–BI magic labeling of star related graphs, IJREAM, 5 (2019), 480–484. https://doi.org/10.35291/2454-9150.2019.0078 doi: 10.35291/2454-9150.2019.0078
[23]	T. S. Martini, D. Indriati, T. A. Kusmayadi, On reverse super edge bimagic labeling of gear graph, hibiscus graph and dovetail graph, Int. J. Comput. Sci. Appl. Math., 10 (2024), 51–55.
[24]	K. Amuthavalli, P. Sugapriya, Reverse super edge-trimagic labeling for star related graphs, MJM, 7 (2019), 519–525. https://doi.org/10.26637/MJM0703/0025 doi: 10.26637/MJM0703/0025
[25]	T. S. Martini, Y. Susanti, On reverse super edge trimagic labeling of dove tail related graphs, AIP Conf. Proc., 3201 (2023), 030009. https://doi.org/10.1063/5.0230966 doi: 10.1063/5.0230966
[26]	R. Frucht, F. Harary, On the corona of two graphs, Aeq. Math., 4 (1970), 322–325. http://doi.org/10.1007/BF01844162 doi: 10.1007/BF01844162

Reader Comments

Your name:*

Email:*
© 2026 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)