Journal of applied mathematics & informatics

  • 제42권1호
  • /
  • Pages.1-14
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  • 2024
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  • 2734-1194(pISSN)
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  • 2234-8417(eISSN)
한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
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PAIR DIFFERENCE CORDIALITY OF CERTAIN SUBDIVISION GRAPHS

  • R. PONRAJ (Department of Mathematics, Sri Paramakalyani College) ;
  • A. GAYATHRI (Department of Mathematics, Manonmaniam Sundaranar University) ;
  • S. SOMASUNDARAM (Department of Mathematics, Manonmaniam Sundaranar University)
  • 투고 : 2021.06.03
  • 심사 : 2023.10.05
  • 발행 : 2024.01.30
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초록

Let G = (V, E) be a (p, q) graph. Define $$\begin{cases}\frac{p}{2},\:if\:p\:is\:even\\\frac{p-1}{2},\:if\:p\:is\:odd\end{cases}$$ and L = {±1, ±2, ±3, ···, ±ρ} called the set of labels. Consider a mapping f : V → L by assigning different labels in L to the different elements of V when p is even and different labels in L to p - 1 elements of V and repeating a label for the remaining one vertex when p is odd.The labeling as defined above is said to be a pair difference cordial labeling if for each edge uv of G there exists a labeling |f(u) - f(v)| such that |Δf1 - Δfc1| ≤ 1, where Δf1 and Δfc1 respectively denote the number of edges labeled with 1 and number of edges not labeled with 1. A graph G for which there exists a pair difference cordial labeling is called a pair difference cordial graph. In this paper we investigate the pair difference cordial labeling behavior of subdivision of some graphs.

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과제정보

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

참고문헌

  1. M. Andar, S. Boxwala, and N. Limaye, Cordial labeling of some wheel related graphs, J. Combin. Math. Combin. Comput. 41 (2002), 203-208.
  2. M. Andar, S. Boxwala, and N. Limaye, New family of cordial graphs, J. Combin. Math. Combin. Comput. 53 (2005), 117-154.
  3. I. Cahit, Cordial Graphs : A weaker version of Graceful and Harmonious graphs, Ars combin. 23 (1987), 201-207.
  4. S. Cichaz, A. Gorich, and Z. Tuza, Cordial labeling of hypertrees, Disc. Math. 313 (2013), 2518-2524. https://doi.org/10.1016/j.disc.2013.07.025
  5. A.T. Diab, Study of some problems of cordial graphs, Ars combin. 92 (2009), 255-261.
  6. A.T. Diab, S. Nada, Some results on specific graphs, Ars combin. 132 (2017), 93-103.
  7. G.M. Du, On the cordiality of the union of wheels, J. Inn. ong. Norm. Univ. Nat. Sci. 37 (2008), 180-181.
  8. J.A. Gallian, A Dynamic survey of graph labeling, The Electronic Journal of Combinatorics 19 (2016).
  9. G.V. Ghodasara, M. Patel, and I.I. Jadav , Cordial labeling of grid related graphs, Internat. J. Comb. Graph Th. and App. 6 (2013), 55-62.
  10. G.V. Ghodasara and Sonchhatra, Cordial labeling of fan related graphs, Internat. J. Sci. Eng. Res. 4 8 (2013), 470-476.
  11. R.L. Graham, and N.J.A. Solane, On additive bases and harmonious graphs, SIAM J. Alg. Discrete Methods 1 (1980), 382-404. https://doi.org/10.1137/0601045
  12. F. Harary, Graph theory, Addision wesley, New Delhi, 1969.
  13. M. Hovey, A-cordial graphs, Discrete Math. 93 (1993), 183-194. https://doi.org/10.1016/0012-365X(91)90254-Y
  14. W.W. Krichher, On the cordiality of some specific graphs, Ars Combinatoria 31 (1991), 127-138.
  15. O. Pechnik, J. Wise, Generalized graph cordiality, Discuss. Math. Grap Th. 32 (2012), 557-567. https://doi.org/10.7151/dmgt.1626
  16. R. Ponraj, A. Gayathri, and S. Soma Sundaram, Pair difference cordial labeling of graphs, J. Math. Comp. Sci. 11 (2021), 2551-2567.
  17. R. Ponraj, A. Gayathri, and S. Soma Sundaram, Pair difference cordiality of some snake and butterfly graphs, Journal of Algorithms and Computation 53 (2021), 149-163.
  18. R. Ponraj, A. Gayathri, and S. Soma Sundaram, Pair difference cordial graphs obtained from the wheels and the paths, J. Appl. and Pure Math. 3 (2021), 97-114.
  19. R. Ponraj, A. Gayathri, and S. Soma Sundaram, Pair difference cordiality of some graphs derived from ladder graph, J. Math. Comp. Sci. 11 (2021), 6105-6124.
  20. R. Ponraj, A. Gayathri, and S. Soma Sundaram, Some pair difference cordial graphs, Ikonion Journal of Mathematics 3 (2021), 17-26.
  21. R. Ponraj, A. Gayathri, and S. Soma Sundaram, Pair difference cordiality of some special graphs, J. Appl. and Pure Math. 3 (2021), 263-274.
  22. R. Ponraj, A. Gayathri, and S. Soma Sundaram, Pair difference cordial labeling of planar grid and mangolian tent, Journal of Algorithms and Computation 53 (2021), 47-56.
  23. R. Ponraj, J.V.X. Parthipan, Pair sum labeling of graphs, J. Indian Acad. Math. 32 (2010), 587-595.
  24. R. Ponraj, S. Sathish narayanan, and R. Kala, Difference cordial labeling of graphs, Global J. Math. Sciences : Theory and Practical 3 (2013), 192-201.
  25. A. Rosa, On certain Valuations of the vertices of a graph,Theory of Graphs, International Symposium, Rome., July, 1967, 349-345.