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4-TOTAL MEAN CORDIAL LABELING OF ARROW GRAPHS AND SHELL GRAPHS

  • R. PONRAJ (Department of Mathematics, Sri Paramakalyani College) ;
  • S. SUBBULAKSHMI (Department of Mathematics, Manonmaniam Sundaranar University)
  • Received : 2023.06.11
  • Accepted : 2023.09.14
  • Published : 2023.11.30

Abstract

In this paper we investigate the 4-total mean cordial labeling behavior of arrow graphs, shell-Butterfly graph and graphs obtained by joining two copies of shell graphs by a path.

Keywords

Acknowledgement

The authors thank the Referee for their valuable suggestions towards the improvement of the paper.

References

  1. M. Andar, S. Boxwala, and N. Limaye, Cordial labelings of some wheel related graphs, J. Combin. Math. Combin. Comput. 41 (2002), 203-208. 
  2. M. Andar, S. Boxwala, and N. Limaye, A note on cordial labelings of multiple shells, Trends Math. (2002), 77-80. 
  3. R. Avudainayaki, B. Selvam, E3- cordial labelings and total 3-sum cordial labeling for the extended duplicate graph of arrow graph, International Journal of Engineering, Science and Mathematics 7 (2018), 50-61. 
  4. M.V. Bapat, Some complete-graph related families of product cordial (pc) graphs, Aryabhatta J. Math. Informatics 09 (2017), 133-140. 
  5. M.V. Bapat, Product cordial labeling of some fusion graphs, Internat. J. Math.Trends and Tech. 50 (2017). 
  6. J. Baskar Babujee and L. Shobana, Prime cordial labelings, Int. Review on Pure and Appl. Math. 5 (2009), 277-282. 
  7. J. Baskar Babujee and L. Shobana, Prime and prime cordial labeling for some special graphs, Int. J. Contemp. Math. Sciences 5 (2010), 2347-2356. 
  8. M.I. Bosmia and K.K. Kanani, Divisor cordial labeling in the context of graph operations on bistar, Global J. Pure and Appl. Math. 12 (2016), 2605-2618. 
  9. I. Cahit, Cordial Graphs: A weaker version of Graceful and Harmonious graphs, Ars Combin. 23 (1987), 201-207. 
  10. U. Deshmukh and V.Y. Shaikh, Mean cordial labelling of some star-related graphs, Internat. J. Math. Combin. 3 (2016), 146-157. 
  11. J. Devaraj, On edge-cordial graphs, Graph Theory Notes of New York, XLVII, (2004), 14-18. 
  12. A.T. Diab, Study of some problems of cordial graphs, Ars Combin. 92 (2009), 255-261. 
  13. J.A. Gallian, A Dynamic survey of graph labeling, The Electronic Journal of Combinatorics 19 (2016), #Ds6. 
  14. Harary, Graph theory, Addision wesley, New Delhi, 1969. 
  15. J. Jeba Jesintha, K. Ezhilarsi Hilda, ρ∗-Labelingof pathsand shell butterfly graphs, International Journal of pure and Applied Mathematics 101 (2015), 645-653. 
  16. P. Jeyanthi and N. Angel Benseera, Totally magic cordial labeling of one-point union of n copies of a graph, Opuscula Math. 34 (2014), 115-133.  https://doi.org/10.7494/OpMath.2014.34.1.115
  17. P. Jeyanthi and N. Angel Benseera, Totally magic cordial labeling of some graphs, J. Algorithms Comput. 46 (2015), 1-8. 
  18. R. Ponraj, S. Sathish Narayanan, A.M.S. Ramasamy, Total Mean cordial labeling of graphs, International J. Math. Combin. 4 (2014), 56-68. 
  19. R. Ponraj, M. Sivakumar, M. Sundaram, Mean cordial labeling of graphs, Open Journal of Discreate mathematics 2 (2012), 145-148.  https://doi.org/10.4236/ojdm.2012.24029
  20. R. Ponraj, S. Subbulakshmi, S. Somasundaram, k-total mean cordial graphs, J. Math. Comput. Sci. 10 (2020), 1697-1711. 
  21. R. Ponraj, S. Subbulakshmi, S. Somasundaram, 4-total mean cordial graphs derived from paths, J. Appl and Pure Math. 2 (2020), 319-329. 
  22. R. Ponraj, S. Subbulakshmi, S. Somasundaram, 4-total mean cordial labeling in subdivision graphs, Journal of Algorithms and Computation 52 (2020), 1-11. 
  23. R. Ponraj, S. Subbulakshmi, S. Somasundaram, Some 4-total mean cordial graphs derived from wheel, J. Math. Comput. Sci. 11 (2021), 467-476. 
  24. R. Ponraj, S. Subbulakshmi, S. Somasundaram, 4-total mean cordial graphs with star and bistar, Turkish Journal of Computer and Mathematics Education 12 (2021), 951-956. 
  25. R. Ponraj, S. Subbulakshmi, S. Somasundaram, On 4-total mean cordial graphs, J. Appl. Math and Informatics 39 (2021), 497-506. 
  26. R. Ponraj, S. Subbulakshmi, S. Somasundaram, 4-total mean cordial labeling of special graphs, Journal of Algorithms and Computation 53 (2021), 13-22. 
  27. R. Ponraj, S. Subbulakshmi, S. Somasundaram, 4-total mean cordial labeling of union of some graphs with the complete bipartite graph K2,n, Journal of Algorithms and Computation 54 (2022), 35-46. 
  28. R. Ponraj, S. Subbulakshmi, S. Somasundaram, 4-total mean cordial labeling of some graphs derived from H-graph and star, International J. Math. Combin. 3 (2022), 99-106. 
  29. S.K. Vaidya and N.B. Vyas, E-cordial labeling for Cartesian product of some graphs, Studies Math. Sci. 3 (2011), 11-15. 
  30. M.Z. Youssef, On Ek-cordial labeling, Ars Combin. 104 (2012), 271-279.