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Irregular Total Labellings of Generalized Petersen Graphs

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Abstract

The total edge irregularity strength tes(G) and total vertex irregularity strength tvs(G) are invariants analogous to irregular strength s(G) of a graph G for total labellings. Bača et al. (Discrete Math. 307:1378–1388, 2007) determined the bounds and precise values for some families of graphs concerning these parameters. In this paper, we show the exact values of the total edge irregularity strength and total vertex irregularity strength of generalized Petersen graphs P(n,k).

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References

  1. Bac̆a, M., Jendrol, S., Miller, M., Ryan, J.: On irregular total labellings. Discrete Math. 307, 1378–1388 (2007)

    Article  MathSciNet  Google Scholar 

  2. Baril, J.L., Kheddouci, H., Togni, O.: The irregularity strength of circulant graphs. Discrete Math. 304, 1–10 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  3. Brandt, S., Mis̆skuf, J., Rautenbach, D.: On a conjecture about edge irregular total labelings. J. Graph Theory 57, 333–343 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bohman, T., Kravitz, D.: On the irregularity strength of trees. J. Graph Theory 45(4), 241–254 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  5. Ivanc̆o, J., Jendrol, S.: The total edge irregularity strength of trees. Discuss. Math., Graph Theory 26(3), 449–456 (2006)

    MathSciNet  Google Scholar 

  6. Jendrol, S., Tkác̆, M.: The irregularity strength of tKp. Discrete Math. 145, 301–305 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  7. Jendrol, S., Z̆oldák, V.: The irregularity strength of generalized Petersen graphs. Math. Slovaca, 45(2), 107–113 (1995)

    MathSciNet  MATH  Google Scholar 

  8. Jendrol, S., Mis̆kuf, J., Soták, R.: Total edge irregularity strength of complete graphs and complete bipartite graphs. Electron. Notes Discrete Math. 28, 281–285 (2007)

    Article  Google Scholar 

  9. Meissner, A., Niwińska, M.A., Zwierzynski, K.T.: Computing an irregularity strength of selected graphs. Electron. Notes Discrete Math. 24, 137–144 (2006)

    Article  Google Scholar 

  10. Togni, O.: Irregularity strength of the toroidal grid. Discrete Math. 165/166, 609–620 (1997)

    Article  MathSciNet  Google Scholar 

  11. Togni, O.: Irregularity strength and compound graphs. Discrete Math. 218, 235–243 (2000)

    Article  MathSciNet  MATH  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Shahjalal University of Science and Technology, Sylhet, 3114, Bangladesh

    Khandoker Mohammed Mominul Haque

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  1. Khandoker Mohammed Mominul Haque
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Correspondence to Khandoker Mohammed Mominul Haque.

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Haque, K.M.M. Irregular Total Labellings of Generalized Petersen Graphs. Theory Comput Syst 50, 537–544 (2012). https://doi.org/10.1007/s00224-011-9350-7

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  • DOI: https://doi.org/10.1007/s00224-011-9350-7

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