Target Set Selection on generalized pancake graphs


Target Set Selection (TSS) was initially proposed to study the problem of the spread of information, ideas or influence through a social network and had formulated many problems arising in various practical applications. We consider a particular type of graphs, namely n-dimensional m-sided pancake graph mPn, which is one class of Cayley graphs and is widely used in the symmetric interconnection networks. We establish a bound of TSS on mPn by the minimum feedback vertex set.

This is a preview of subscription content, log in to check access.


  1. 1.

    E. Ackerman, O. Ben-Zwi, and G. Wolfovitz, Combinatorial model and bounds for target set selection, Theoret. Comput. Sci., 411 (2010), 4017–4022.

    MathSciNet  Article  Google Scholar 

  2. 2.

    S. S. Adams, Z. Brass, C. Stokes, and D. S. Troxell, Irreversible k-threshold and majority conversion processes on complete multipartite graphs and graph products, Australas. J. Combin., 56 (2013), 47–60.

    MathSciNet  MATH  Google Scholar 

  3. 3.

    S. S. Adams, D. S. Troxell, and S. L. Zinnen, Dynamic monopolies and feedback vertex sets in hexagonal grids, Comput. Math. Appl., 62 (2011), 4049–4057.

    MathSciNet  Article  Google Scholar 

  4. 4.

    S. Bao and L. W. Beineke, The decycling number of graphs, Australas. J. Combin., 25 (2002), 285–298.

    MathSciNet  MATH  Google Scholar 

  5. 5.

    O. Ben-Zwi, D. Hermelin, and D. Lokshtanov, An exact almost optimal algorithm for target set selection in social networks, Proceedings of the tenth ACM conference on Electronic commerce, 2009, Stanford, CA, USA.

    Google Scholar 

  6. 6.

    L. Beineke and R. Vandell, Decycling graphs, J. Graph Theory, 25 (1997), 59–77.

    MathSciNet  Article  Google Scholar 

  7. 7.

    E. Berger, Dynamic monopolies of constant size, J. Combin. Theory Ser. B, 83 (2001), 191–200.

    MathSciNet  Article  Google Scholar 

  8. 8.

    N. Chen, On the approximability of influence in social networks, SIAM J. Discrete Math., 23 (2009), 1400–1415.

    MathSciNet  Article  Google Scholar 

  9. 9.

    C. Y. Chiang, L. H. Huang, and H. G. Yeh. Target set selection problem for honeycomb networks, SIAM J. Discrete Math., 27 (2013), 310–328.

    MathSciNet  Article  Google Scholar 

  10. 10.

    C. Y. Chiang, L. H. Huang, B. J. Li, J. Wu, and H. G. Yeh, Some results on the target set selection problem, J. Comb. Optim., 25 (2011), 702–715.

    MathSciNet  Article  Google Scholar 

  11. 11.

    M. Chopin, A. Nichterlein, R. Niedermeier, and M. Weller, Constant thresholds can make target set selection tractable, Theory. Comput. Systems, 55 (2014), 61–83.

    MathSciNet  Article  Google Scholar 

  12. 12.

    P. Compeau, Girth of pancake graphs, Discrete Appl. Math., 159 (2011), 1641–1645.

    MathSciNet  Article  Google Scholar 

  13. 13.

    P. Domingos and M. Richardson, Mining the network value of customers, Seventh International Conference on Knowledge Discovery and Data Mining, 2001, San Francisco, CA, USA.

    Google Scholar 

  14. 14.

    P. A. Dreyer and F. S. Roberts, Irreversible k-threshold processes: Graph-theoretical threshold models of the spread of disease and of opinion, Discrete Appl. Math., 157 (2009), 1615–1627.

    MathSciNet  Article  Google Scholar 

  15. 15.

    T. Iwasaki, Fault-tolerant routing in burnt pancake graphs, Inform. Process. Lett., 110 (2010), 535–538.

    MathSciNet  Article  Google Scholar 

  16. 16.

    P. Festa, P. Pardalos, and Mauricio G. C. Resende, Feedback set problems, Springer, US, (1999).

    Google Scholar 

  17. 17.

    P. Flocchini, R. Královič, P. Ruzicka, and N. Santoro, On time versus size for monotone dynamic monopolies in regular topologies, J. Discrete Algorithms, 2 (2002), 135–156.

    MATH  Google Scholar 

  18. 18.

    P. Flocchini, E. Lodi, F. Luccio, L. Pagli, and N. Santoro, Dynamic monopolies in tori, Discrete Appl. Math., 137 (2004), 197–212.

    MathSciNet  Article  Google Scholar 

  19. 19.

    M. Heydari and I. Sudborough, On sorting by prefix reversals and the dimaeter of pancake networks, Parallel Archirectures and Their Efficient Use, Lecture Notes in Computer Science, 678 (1993), 218–227.

    Article  Google Scholar 

  20. 20.

    C. Hoffman, Group theoretic algorithms and graph isomorphism, Springer, New York (1982).

    Google Scholar 

  21. 21.

    S. Jung and K. Kaneko, A feedback vertex set on pancake graphs, International Conference on Parallel and distributed Processing Techniques and Applications, 2010, San Francisco, CA, USA.

    Google Scholar 

  22. 22.

    M. Justan, F. Muga II, and I. Sudborough, On the generalization of the pancake network, Proceedings of the International Symposium on Parallel Archiectures, Algorithms and Networks, 2002, Sydney, Australia.

    Google Scholar 

  23. 23.

    K. Kaneko and Y. Suzuki, Node-to-set disjoint paths problem in pancake graphs, IEICE Trans. Inf. Syst., E86-D (2003), 1628–1633.

    Google Scholar 

  24. 24.

    D. Kempe, J. Kleinberg, and E. Tardos, Maximizing the spread of influence through a social network, In Proceedings of the 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2003, London, UK.

    Google Scholar 

  25. 25.

    F. Luccio, Almost exact minimum feedback vertex set in meshes and butterflies, Inform. Process. Lett., 66 (1998), 59–64.

    MathSciNet  Article  Google Scholar 

  26. 26.

    D. Peleg, Local majorities, coalitions and monopolies in graphs: A review, Theoret. Comput. Sci., 282 (2002), 231–257.

    MathSciNet  Article  Google Scholar 

  27. 27.

    D. A. Pike and Y. Zou, Decycling Cartesian products of two cycles, SIAM J. Discrete Math., 19 (2005), 651–663.

    MathSciNet  Article  Google Scholar 

  28. 28.

    M. Zaker, On dynamic monopolies of graphs with general thresholds, Discrete Math., 312 (2012), 1136–1143.

    MathSciNet  Article  Google Scholar 

Download references


My deepest gratitude goes to the anonymous reviewers for their careful work and thoughtful suggestions that have helped improve this paper substantially.

Author information



Corresponding author

Correspondence to Haining Jiang.

Additional information

This work was supported by the Doctoral Foundation of Heze University (Grant numbers, XY18BS12).

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Jiang, H. Target Set Selection on generalized pancake graphs. Indian J Pure Appl Math 51, 379–389 (2020).

Download citation

Key words

  • Target set selection
  • feedback vertex set
  • n-dimensional m-sided pancake graph

2010 Mathematics Subject Classification

  • 05Cxx
  • 68R10