On Edge Irregularity Strength of Mycielskian of Paths and Cycles

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Authors

  • Umme Salma
     Department of Science and Humanities, PES University, Bangalore ,IN
  • H. M. Nagesh
     Department of Science and Humanities, PES University, Bengaluru – 560085, Karnataka ,IN
  • B. Azghar Pasha
     Department of Mathematics, M. S. Ramaiah Institute of Technology, Bengaluru – 560054, Karnataka ,IN
  • N. Narahari
     Department of Mathematics, University College of Science, Tumkuru University, Tumakuru – 572103, Karnataka ,IN

DOI:

https://doi.org/10.18311/jmmf/2023/43610

Keywords:

Edge Irregularity Strength, Mycielskian of Paths and Cycles.

Abstract

For a graph G having no loops and parallel edges, a labeling on the vertex set of G,Ψ:V(G)→{1,2,…,α} is refers to α-labeling. Let ab∈G be an edge. Then the weight the edge ab is zΨ (ab)=Ψ(a)+Ψ(b). An α-labeling on the vertex set of G is refers to be an edge irregular α-labeling of G if zΨ (a)≠zΨ (b),where a≠b in G. The least number α for which the graph G has an edge irregular α-labeling is referred to the edge irregularity strength of G, written es(G). The edge irregularity strength of Mycielskian of paths and cycles is computed.

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Published

2024-05-24

How to Cite

Salma, U., Nagesh, H. M., Azghar Pasha, B., & Narahari, N. (2024). On Edge Irregularity Strength of Mycielskian of Paths and Cycles. Journal of Mines, Metals and Fuels, 71(12A), 208–213. https://doi.org/10.18311/jmmf/2023/43610

Issue

Volume 71, Issue 12A , 2023

Section

Articles

License

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

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References

Chartrand G, Jacobson MS, Lehel J, Oellermann OR, Saba F. Irregular networks. Congressus Numerantium. 1988; 64:187-192.

Ahmad A, Al-Mushayt O, Baca M. On edge irregularity strength of graphs. Appl Math Comput. 2014; 243:607- 10. https://doi.org/10.1016/j.amc.2014.06.028 DOI: https://doi.org/10.1016/j.amc.2014.06.028

Lin W, Wu J, Lam PCB, Gu G. Several parameters of generalized Mycielskians. Discrete Appl Math. 2006; 154:1173-82. https://doi.org/10.1016/j.dam.2005.11.001 DOI: https://doi.org/10.1016/j.dam.2005.11.001

Ahmad A, Baca M, Nadeem MF. On the edge irregularity strength of Toeplitz graphs. Sci Bull Politeh Univ Buchar. 2018; 78:155-62.

Tarawneh I, Hasni R, Ahmad A. On the edge irregularity strength of corona product of graphs with paths. Appl Math E-Notes. 2016; 16:80-7.

Tarawneh I, Hasni R, Asim MA, Siddiqui MA. On the edge irregularity strength of disjoint union of graphs. Ars Combinatoria. 2019; 142:239-49.

Salma U, Nagesh HM. On the edge irregularity strength of sunlet graph. Bull Int Math Virtual Inst. 2022; 12(2):213- 17.

Nagesh HM, Girish VR. On edge irregularity strength of line graph and line cut-vertex graph of comb graph. Notes on Number Theory and Discrete Mathematics. 2022; 28(3):517-524. https://doi.org/10.7546/nntdm. 2022.28.3.517-524 DOI: https://doi.org/10.7546/nntdm.2022.28.3.517-524

Ahmad A, Bokhary U, Ahtsham S, Imaran M, BaigAQ. Vertex irregular labelings of cubic graphs. Util Math. 2013; 91:287-99.

Ahmad A, Baca M. On vertex irregular total labeling. Ars Combin. (in press).

Aigner M, Triesch E. Irregular assignemnts of trees and forests. SIAM J Discrete Math. 1991; 3(4). https://doi. org/10.1137/0403038 DOI: https://doi.org/10.1137/0403038

Al-Mushayt O. Irregular assignemnts of trees of certain families of graph with path P2. Ars Combin. (in press). 13. Amar D, Togni O. Irregualr strength of trees. Discrete Math. 1998; 190:15-38. https://doi.org/10.1016/S0012- 365X(98)00112-5 DOI: https://doi.org/10.1016/S0012-365X(98)00112-5

Bohman T, Kravitz D. On the irregularity strength of trees. J Graph Theory. 2004; 45:241-54. https://doi.org/10.1002/jgt.10158 DOI: https://doi.org/10.1002/jgt.10158

Baca M, Jendrol S, Miller M, Ryan J. On irregular total labellings. Discrete Math. 2007; 307:1378-88. https://doi. org/10.1016/j.disc.2005.11.075 DOI: https://doi.org/10.1016/j.disc.2005.11.075

Cammack LA, Schelp RH, Schrag GC. Irregularity strength of full d-ary trees. Congr Number. 1991; 81:113-19.

Dimitz JH, Garnick DK, Gyarfas A. On the irregularity strength of the mxn grid. J Graph Theory. 1992; 16:355- 74. https://doi.org/10.1002/jgt.3190160409 DOI: https://doi.org/10.1002/jgt.3190160409

Frieze A, Gould RJ, Karonski M, Pfender F. On graph irregularity strength. J Graph Theory; 2002: 41:120-37. https://doi.org/10.1002/jgt.10056 DOI: https://doi.org/10.1002/jgt.10056

Nierhoff T. A tight bound on the irregularity strength of graphs. SIAM J Discrete Math. 2000; 13:313-23. https:// doi.org/10.1137/S0895480196314291 DOI: https://doi.org/10.1137/S0895480196314291

Przybylo J. Linear bound on the irregularity strength and total vertex irregularity strength of graphs. SIAM J Discrete Math. 2008; 23:511-16. https://doi. org/10.1137/070707385 DOI: https://doi.org/10.1137/070707385