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PAIR MEAN CORDIAL LABELING OF GRAPHS OBTAINED FROM PATH AND CYCLE

  • PONRAJ, R. (Department of Mathematics, Sri Paramakalyani College) ;
  • PRABHU, S. (Department of Mathematics, Sri Paramakalyani College)
  • 투고 : 2022.04.04
  • 심사 : 2022.06.30
  • 발행 : 2022.07.30

초록

Let a graph G = (V, E) be a (p, q) graph. Define $${\rho}\;=\;\{\array{{\frac{p}{2}}&p\text{ is even}\\{\frac{p-1}{2}}\;&p\text{ is odd,}}$$ and M = {±1, ±2, ⋯ ± 𝜌} called the set of labels. Consider a mapping λ : V → M by assigning different labels in M to the different elements of V when p is even and different labels in M 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 mean cordial labeling if for each edge uv of G, there exists a labeling $\frac{{\lambda}(u)+{\lambda}(v)}{2}$ if λ(u) + λ(v) is even and $\frac{{\lambda}(u)+{\lambda}(v)+1}{2}$ if λ(u) + λ(v) is odd such that ${\mid}\bar{\mathbb{S}}_{{\lambda}_1}-\bar{\mathbb{S}}_{{\lambda}^c_1}{\mid}{\leq}1$ where $\bar{\mathbb{S}}_{{\lambda}_1}$ and $\bar{\mathbb{S}}_{{\lambda}^c_1}$ respectively denote the number of edges labeled with 1 and the number of edges not labeled with 1. A graph G for which there exists a pair mean cordial labeling is called a pair mean cordial graph. In this paper, we investigate the pair mean cordial labeling of graphs which are obtained from path and cycle.

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과제정보

The authors thank the Referee for the 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. Compt. 41 (2002), 203-208.
  2. M. Andar, S. Boxwala and N. Limaye, A note on cordial labeling of multiple shells, Trends Math. (2002), 77-80.
  3. M. Andar, S. Boxwala and N. Limaye, On the Cordiality of the t-uniform homeomorphs-I, Ars Combin. 66 (2003), 313-318.
  4. M. Andar, S. Boxwala and N. Limaye, New families of cordial graphs, J. Combin. Math. Combin. Compt. 53 (2005), 117-154.
  5. I. Cahit, Cordial graphs: a weaker versionof graceful and harmonious graphs, Ars comb. 23 (1987), 201-207.
  6. I. Cahit, H-Cordial graphs, Bull. Inst. Combin. Appl. 18 (1996), 87-101.
  7. G. Chartrand, S.M. Lee and P. Zhang, Uniformly cordial graphs, Discrete Math. 306 (2006), 726-737. https://doi.org/10.1016/j.disc.2005.11.025
  8. A.T. Diab, A study of some problems of cordial graphs, Ars Combin. 92 (2009), 255-261.
  9. A.T. Diab, On Cordial labeling of some results on cordial graphs, Ars Combin. 99 (2011), 161-173.
  10. A.T. Diab and E. Elsakhawi, Some results on cordial graphs, Proc. Maths. Phys. Soc. Egypt. 77 (2002), 67-87.
  11. J.A. Gallian, A dynamic survey of graph labeling, The Electronic Journal of Combinatorics 24 (2021).
  12. F. Harary, Graph theory, Addison Wesely, Reading Mass., 1972.
  13. M. Hovey, A-cordial graphs, Discrete Math. 93 (1991), 183-194. https://doi.org/10.1016/0012-365X(91)90254-Y
  14. R. Ponraj, A. Gayathri and S. Somasundaram, Pair difference cordial labeling of graphs, J. Math. Compt. Sci. 11 (2021), 2551-2567.
  15. R. Ponraj, A. Gayathri and S. Somasundaram, Some pair difference cordial graphs, Ikonion Journal of Mathematics 3 (2021), 17-26.
  16. R. Ponraj and S. Prabhu, Pair mean cordial labeling of graphs, Journal of Algorithms and Computation 54 (2022), 1-10.
  17. S. Somasundaram and R. Ponraj, Mean labeling of graphs, National Academy Science Letter 26 (2003), 210-213.