Edge irregularity strength of certain families of comb graph

• Zhang, Xiujun ^[1] ; Cancan, Murat ^[2] ; Nadeem, Muhammad Faisal ^[3] ; Imran , Muhammad
  1. [1] Chengdu University

     Chengdu University

     China

     
  2. [2] Yüzüncü Yıl University

     Yüzüncü Yıl University

     Turquía

     
  3. [3] COMSATS Institute of Information Technology

     COMSATS Institute of Information Technology

     Pakistán

     

  Mostrar afiliaciones +
• 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. 787-797
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-2020-04-0049
• Enlaces
  • Texto completo
• Resumen

  • Edge irregular mapping or vertex mapping h : V (U ) ?? {1, 2, 3, 4, ..., s} is a mapping of vertices in such a way that all edges have distinct weights. We evaluate weight of any edge by using equation wth(cd) = h(c)+h(d), ?c, d ? V (U ) and ?cd ? E(U ). Edge irregularity strength denoted by es(U ) is a minimum positive integer use to label vertices to form edge irregular labeling. In this paper, we find exact value of edge irregularity strength of different families of comb graph.

• Referencias bibliográficas
  • A. Ahmad, M. Arshad, and G. Izarikova, “Irregular labelings of helm and sun graphs”, AKCE international journal of graphs and combinatorics,...
  • A. Ahmad, O. B. S. Al-Mushayt, and M. Baca, “On edge irregularity strength of graphs”, Applied mathematics and computation, vol. 243, pp....
  • A. Ahmad, M. Ba?a, Y. Bashir, M. K. Siddiqui, “Total edge irregularity strength of strong product of two paths”, Ars combinatoria, vol. 106,...
  • A. Ahmad, M. Ba?a, and M. K. Siddiqui, “On edge irregular total labeling of categorical product of two cycles”, Theory of computing systems,...
  • A. Ahmad, M. Ba?a, M., M. F. Nadeem, “On edge irregularity strength of Toeplitz graphs”, Scientific Bulletin - "Politehnica" University...
  • O. B. S. Al-Mushayt, “On edge irregularity strength of products of certain families of graphs with path P-2”, Ars combinatoria, vol. 135,...
  • O. B. S. Al-Mushayt, A. Ahmad, M. K. Siddiqui, “On the total edge irregularity strength of hexagonal grid graphs”, Australasian journal combinatorics,...
  • D. Amar and O. Togni, “Irregularity strength of trees”, Discrete mathematics, vol. 190, no. 1-3, pp. 15–38, Aug. 1998, doi: 10.1016/s0012-365x(98)00112-5
  • M. Anholcer, M. Kalkowski, and J. Przybyo, “A new upper bound for the total vertex irregularity strength of graphs”, Discrete mathematics,...
  • M. Ba?a, S. Jendrol, M. Miller, and J. Ryan, “On irregular total labellings”, Discrete mathematics, vol. 307, no. 11-12, pp. 1378-1388, May...
  • M. Ba?a and M. K. Siddiqui, “Total edge irregularity strength of generalized prism”, Applied mathematics and computation, vol. 235, pp. 168-173,...
  • T. Bohman and D. Kravitz, “On the irregularity strength of trees”, Journal of graph theory, vol. 45, no. 4, pp. 241-254, 2004, doi: 10.1002/jgt.10158
  • G. Chartrand, M. S. Jacobson, J. Lehel, O. R. Oellermann, S. Ruiz, F. Saba, “Irregular networks”, Congressus numerantium, vol. 64, pp. 187-192,...
  • A. Frieze, R. J. Gould, M. Karoski, and F. Pfender, “On graph irregularity strength”, Journal of graph theory, vol. 41, no. 2, pp. 120-137,...
  • K. M. M. Haque, “Irregular total labellings of generalized Petersen graphs”, Theory of computing systems, vol. 50, no. 3, pp. 537-544, Jul....
  • J. Ivanco and S. Jendrol, “Total edge irregularity strength of trees”, Discussiones mathematicae graph theory, vol. 26, no. 3, p. 449, 2006,...
  • S. Jendrol, J. Miskuf, and R. Sotak, “Total edge irregularity strength of complete graphs and complete bipartite graphs”, Discrete mathematics,...
  • M. Kalkowski, M. Karonski, and F. Pfender, “A new upper bound for the irregularity strength of graphs”, SIAM journal on discrete mathematics,...
  • J. Liu, J. Zhao, and Z. Zhu, “On the number of spanning trees and normalized Laplacian of linear octagonal quadrilateral networks”, International...
  • P. Majerski and J. Przybylo, “Total vertex irregularity strength of dense graphs”, Journal of graph theory, vol. 76, no. 1, pp. 34-41, Jul....
  • Nurdin, E. T. Baskoro, A. N. M. Salman, and N. N. Gaos, “On the total vertex irregularity strength of trees”, Discrete mathematics, vol. 310,...
  • J. Przybylo, “Linear bound on the irregularity strength and the total vertex irregularity strength of graphs”, SIAM journal on discrete mathematics,...
  • I. Tarawneh, R. Hasni, and A. Ahmad, “On the edge irregularity strength of corona product of cycle with isolated vertices”, AKCE international...
  • H. Yang, M. A. Rashid, S. Ahmad, M. K. Siddiqui, and M. F. Hanif, “Cycle super magic labeling of pumpkin, octagonal and hexagonal graphs”,...