Edge even graceful labeling of torus grid graph

• Daoud, Salama Nagy ^[1] ; Saleh, Wedad
  1. [1] Menoufia University

     Menoufia University

     Egipto

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 39, Nº. Extra 4, 2020 (Ejemplar dedicado a: Special Issue: Mathematical Computation in Combinatorics and Graph Theory; i), págs. 1033-1082
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-2020-04-0065
• Enlaces
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• Resumen

  • We study the family of torus grid graphs. We also obtain necessary and sufficent conditions to be edge even graceful labeling for all of the cases of every member of this family.

• Referencias bibliográficas
  • B. D. Acharya, S. Arumugam, and A. Rosa, Eds., Labelings of discrete structures and applications. New Delhi: Narosa, 2008.
  • M. Alaeiyan and M. R. Farahani, “The 1-2-3-edge labeling and vertex colors”, International journal of applied mathematics and machine learning,...
  • G. S. Bloom, “Numbered undirected graphs and their uses. A survey of a unifying scientific and engineering concept and its use in developing...
  • G. S. Bloom and S. W. Golomb, “Applications of numbered undirected graphs”, Proceedings of the IEEE, vol. 65, no. 4, pp. 562-570, Apr. 1977,...
  • G. S. Bloom and S. W. Golomb, “Numbered complete graphs, unusual rulers, and assorted applications”, in Theory and applications of graphs,...
  • G. S. Bloom and D. F. Hsu, “On graceful digraphs and a problem in network addressing”, Congressus numerantium, vol. 35, pp. 91-103, 1982.
  • S. N. Daoud, “Edge odd graceful labeling of some path and cycle related graphs”, AKCE international journal of graphs and combinatorics, vol....
  • S. N. Daoud, “Edge odd graceful labeling Cylinder grid and Torus grid graphs”, IEEE access , vol. 7, pp. 10568-10592, 2018, doi.org/10.1109/access.2018.2889293
  • S. N. Daoud, “Edge even graceful labeling polar grid graph”, Symmetry, vol. 11, no. 1, Art ID. 38, Jan. 2019, doi.org/10.3390/sym11010038
  • S. N. Daoud, “Vertex odd graceful labeling”, Ars combinatoria, vol. 142 , pp. 65-87, 2019. [On line]. Available: https://bit.ly/2Ob4gMN
  • A. Elsonbaty and S. N. Daoud, “Edge even graceful labeling of some path and cycle related graphs”, Ars combinatoria, vol. 130, no. 2, pp....
  • M. R. Farahani, “On the 1-2-3-edge weighting and vertex coloring of complete graph”, International journal of computational sciences &...
  • M. R. Farahani and S. H. Hosseini, “The 1-2-3-edge labeling and vertex coloring of complete graph Kn with a modified algorithm”, Algebras,...
  • J. A. Gallian, “Graph labeling”, The electronic journal of combinatorics, vol. DS6, Dec. 2017, doi: 10.37236/27
  • Z. Gao, “Odd graceful labelings of some union graphs”, Journal of natural science of Heilongjiang University, no. 1, pp. 35 -39, 2007. [On...
  • R. B. Gnanajothi, “Topics in graph theory”, Ph. D. Thesis, Madurai Kamaraj University, 1991.
  • S. W. Golomb, “How to number a graph”, in Graph theory and computing, R. C. Read, Ed., New York, NY: Academic Press, 1972, pp. 23-37, doi:...
  • R. L. Graham and H. O. Pollak, “On the addressing problem for loop switching”, The Bell system technical journal, vol. 50. no. 8, 1971, pp....
  • J. Gross and J. Yellen, Graph theory and its applications, Philadelphia, PA: CRC Press, 1999.
  • Q. Kuan, S. Lee, J. Mitchem, and A. Wang, “On edge-graceful unicyclic graphs”, Congressus numerantium, vol. 61, pp. 65-74, 1988.
  • L. Lee, S. Lee, and G. Murty, “On edge-graceful labelings of complete graphs solution of Lo’s conjecture”, Congressus numerantium, vol. 62,...
  • [22] Li Yan, Yingfang Li, Xiujun Zhang, Madiha Saqlain, Sohail Zafar, and. M. R. Farahani, “Total edge product cordial labeling of some new...
  • S. P. Lo, “On edge-graceful labelings of graphs”, Congressus numerantium, vol. 50, pp. 231-241, 1985.
  • A. Rosa, “On certain valuations of the vertices of a graph,” in Theory of Graphs, International Symposium, Rome, July 1966, New York, NY:...
  • M. A. Seoud and M. E. Abdel-Aal, “On odd graceful graphs”, Ars combinatoria, vol. 108, pp. 161-185, 2013.
  • Y. Shang, “Geometric assortative growth model for small-world networks”, The scientific world journal, vol. 2014, Art ID. 59391, Jan. 2014,...
  • Y. Shang, “More on the normalized Laplacian Estrada index”, Applicable analysis and discrete mathematics, vol. 8, no. 2, pp. 346-357, 2014,...
  • A. Solairaju and K. Chithra, “Edge-odd graceful graphs”, electronic notes in discrete mathematics, vol. 33, pp. 15-20, Apr. 2009, doi: 10.1016/j.endm.2009.03.003
  • M. Sutton, “Summable graphs labellings and their applications”, Ph. D. Thesis, The University of Newcastle, Callaghan, 2001.
  • H. Yang, M. A. Rashid, S. Ahmad, M. K. Siddiqui, and M. F. Hanif, “Cycle super magic labeling of pumpkin, octagonal and hexagonal graphs”,...