Odd harmonious labeling of grid graphs

• Jeyanthi, P. ^[2] ; Philo, S. ^[1] ; Youssef, Maged Z. ^[3]
  1. [1] Manonmaniam Sundaranar University

     Manonmaniam Sundaranar University

     India

     
  2. [2] Govindammal Aditanar College for Women.
  3. [3] Imam Mohammad Ibn Saud Islamic University.

  Mostrar afiliaciones +
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 38, Nº. 3, 2019, págs. 411-428
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-2019-03-0027
• Enlaces
  • Texto completo
• Resumen

  • A graph G(p, q) is said to be odd harmonious if there exists an injection f : V (G) → {0, 1, 2, · · · , 2q − 1} such that the induced function f* : E(G) → {1, 3, · · · , 2q − 1} defined by f∗ (uv) = f (u) + f (v) is a bijection. In this paper we prove that path union of t copies of Pm×Pn, path union of t different copies of Pmᵢ×Pnᵢ where 1 ≤ i ≤ t, vertex union of t copies of Pm×Pn, vertex union of t different copies of Pmᵢ×Pnᵢ where 1 ≤ i ≤ t, one point union of path of Ptn (t.n.Pm×Pm), t super subdivision of grid graph Pm×Pn are odd harmonious graphs.

• Referencias bibliográficas
  • J. Gallian, “A Dynamic Survey of Graph Labeling”, 20th ed. The Electronics Journal of Combinatorics, vol. # DS6, p. 432, 2007. [On line]....
  • R. Graham and N. Sloane, “On Additive Bases and Harmonious Graphs”, SIAM Journal on Algebraic Discrete Methods, vol. 1, no. 4, pp. 382–404,...
  • F. Harary, Graph theory. Reading, MA: Addison-Wesley, 1972.
  • Z. Liang and Z. Bai, “On the odd harmonious graphs with applications”, Journal of Applied Mathematics and Computing, vol. 29, no. 1-2, pp....
  • P. Jeyanthi, S. Philo and K. Sugeng, “Odd harmonious labeling of some new families of graphs”, SUT Journal of Mathematics, vol. 51, no. 2,...
  • P. Jeyanthi and S. Philo, “Odd harmonious labeling of some cycle related graphs”, Proyecciones (Antofagasta), vol. 35, no. 1, pp. 85–98, Mar....
  • P. Jeyanthi and S. Philo, “Odd Harmonious Labeling of Plus Graphs”, Bulletin of the International Mathematical Virtual Institute , vol. 7,...
  • P. Jeyanthi, S. Philo, and M. K. Siddiqui, “Odd harmonious labeling of super subdivisión graphs”, Proyecciones (Antofagasta), vol. 38, no....
  • P. Jeyanthi and S. Philo, “Odd Harmonious Labeling of Some New Graphs”, Southeast Asian Bulletin of Mathematics, vol. 43, no. 4, pp. 509-523,...
  • P. Jeyanthi and S. Philo, "Odd Harmonious Labeling of Subdivided Shell Graphs", International Journal of Computer Sciences and Engineering,...
  • P. Jeyanthi and S. Philo, “Odd Harmonious Labeling of Certain Graphs”, Journal of Applied Science and Computations, vol. 6, no.4, pp. 1224-1232,...
  • P. Jeyanthi and S. Philo, “Some Results on Odd Harmonious Labeling”, Bulletin of the International Mathematical Virtual Institute, vol. 9,...
  • P. Selvaraju, P. Balaganesan and J. Renuka, “Odd Harmonious Labeling of Some Path Related Graphs”, International J. of Math. Sci. & Engg....
  • S. Vaidya and N. Shah, “Some New Odd Harmonious Graphs”, International Journal of Mathematics and Soft Computing, vol. 1, no. 1 pp. 9-16,...
  • S. Vaidya and N. Shah, “Odd Harmonious Labeling of Some Graphs”, International Journal of Mathematical Combinatorics, vol. 3, pp. 105-112,...