Open Access
A
On the super (a, d)-H-antimagic total labelings of three graphs
Dongxu ZhuSchool of Mathematical Sciences Hebei Normal University Shijiazhuang 050024 ChinaView full profile → , *Zhihe LiangCorresponding authorzhiheliang@163.comSchool of Mathematical Sciences Hebei Normal University Shijiazhuang 050024 ChinaSchool of Mathematical Sciences Hebei Normal UniversityShijiazhuang, 050024, ChinaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 05 May 2021
- Accepted:
- 05 Aug 2021
- Published Online:
- 01 Mar 2023
- Article type:
- A
- Language:
- EN
- Article no.:
- JIOS-1031
- Pages:
- 195–205
Abstract
The conception of (a, d)-H-super antimagic total labeling is generated by graph covering, magic square and graph labeling. In this paper we study the (a, d)-H-super antimagic total labelings of the friendship graph Fn, wheel Wn and the graph mG.
Keywords
Subject Classifications
05B3005C78
References
[1] A. Kotzig, A. Rosa, Magic valuations of finite graphs, Canad. Math. Bull., 13 (1970), 451-461.[2] R. Simanjuntak, F. Bertault, M. Miller, Two new(a, d)-antimagic graph labelings, in: Proceedings of 11th Australian Workshop ofCombinatorial Algorithm, (2000), 179-189.[3] Dongxu Zhu, Zhihe Liang, On the super (a, d)-H-antimagic total labelings of path chain graphs, Journal of Information and Optimization Sciences, 42(3) (2021), 689-700.[4] A. Rohini, M. Venkatachalam, Irregular colorings of friendship graph families, Journal of Discrete Mathematical Sciences and Cryptography, 23(4) (2020), 913-924.[5] Melaku Berhe Belay, Chunxiang Wang, Abdul Jalil M. Khalaf, Hamid Hosseini, Mohammad Reza Farahani, Topological indices of the subdivision graph and the line graph of subdivision graph of the wheel graph, Journal of Discrete Mathematical Sciences and Cryptography, 24(2) (2021), 589-601.[6] Z. Liang, Super (a, d)-edge-antimagic total labelings of the complete bipartite graphs, Front. Math. China, 13(1) (2018), 129-146.[7] Z. Liang, On the G-supermagic coverings of graphs, Acta Mathematicae Applicatae Sinica (Chinese Series), 37(5) (2014), 857-864.[8] J. A. Gallian, A dynamic survey of graph labelings, Electron. J. Combin., (2017) # DS6, http://www.combinatorics.org/surveys/ds6.pdf.[9] J. M. Vilarnau, Graph labeling and graph decompositions by partitioning sets of integers, Thesis of Universitat Politècnica de Catalunya, 2010.[10] M. Bača, Y. Lin, M. Miller, M. Z. Youssef, Edge-antimagic graphs, Discrete Math., 307 (2007), 1232-1244.[11] Slamin, M. Bača, Y. Lin, et al. Edge-magic total labelings of wheels, fans and friendship graphs, Bull. Inst. Combin. Appl., 35 (2002), 89-98.[12] M. Nalliah, Super (a, d)-edge antimagic total labelings of friendship graphs, Aus- tralasian Journal of Combinatorics, 53 (2012), 237-243.[13] M. Bača, Z. Kimáková, A. Semanicová-Fenovciková, M. A. Umar, Tree-Antimagicness of Disconnected graphs, Mathematical Problems in Engineering, 2015. http://dx.doi.org/10.1155/2015/504251[14] H. Cohen, Number Theory, Volume I: Tools and Diophantine equations, Springer, New York, (2007), 339-340.
Views: 170Downloads: 7Citations: 0
