IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v191y2008i3p661-676.html
   My bibliography  Save this article

Variable neighborhood search for extremal graphs. 16. Some conjectures related to the largest eigenvalue of a graph

Author

Listed:
  • Aouchiche, M.
  • Bell, F.K.
  • Cvetkovic, D.
  • Hansen, P.
  • Rowlinson, P.
  • Simic, S.K.
  • Stevanovic, D.

Abstract

We consider four conjectures related to the largest eigenvalue of (the adjacency matrix of) a graph (i.e., to the index of the graph). Three of them have been formulated after some experiments with the programming system AutoGraphiX, designed for finding extremal graphs with respect to given properties by the use of variable neighborhood search. The conjectures are related to the maximal value of the irregularity and spectral spread in n-vertex graphs, to a Nordhaus-Gaddum type upper bound for the index, and to the maximal value of the index for graphs with given numbers of vertices and edges. None of the conjectures has been resolved so far. We present partial results and provide some indications that the conjectures are very hard.

Suggested Citation

  • Aouchiche, M. & Bell, F.K. & Cvetkovic, D. & Hansen, P. & Rowlinson, P. & Simic, S.K. & Stevanovic, D., 2008. "Variable neighborhood search for extremal graphs. 16. Some conjectures related to the largest eigenvalue of a graph," European Journal of Operational Research, Elsevier, vol. 191(3), pages 661-676, December.
    • Handle: RePEc:eee:ejores:v:191:y:2008:i:3:p:661-676
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(07)00124-5
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hansen, Pierre & Mladenovic, Nenad, 2001. "Variable neighborhood search: Principles and applications," European Journal of Operational Research, Elsevier, vol. 130(3), pages 449-467, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Mauro Napoletano & Stefano Battiston & Michael König & Frank Schweitzer, 2008. "The efficiency and evolution of R&D Networks," Sciences Po publications 2008-31, Sciences Po.
    2. Michael D. König & Claudio J. Tessone & Yves Zenou, 2010. "From Assortative To Dissortative Networks: The Role Of Capacity Constraints," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 13(04), pages 483-499.
    3. , D. & Tessone, Claudio J. & ,, 2014. "Nestedness in networks: A theoretical model and some applications," Theoretical Economics, Econometric Society, vol. 9(3), September.
    4. repec:hal:spmain:info:hdl:2441/9935 is not listed on IDEAS
    5. Fernando, Garcia Alvarado & Antoine, Mandel, 2022. "The network structure of global tax evasion evidence from the Panama papers," Journal of Economic Behavior & Organization, Elsevier, vol. 197(C), pages 660-684.
    6. repec:hal:wpspec:info:hdl:2441/9935 is not listed on IDEAS
    7. repec:hal:spmain:info:hdl:2441/9933 is not listed on IDEAS
    8. König, Michael D. & Battiston, Stefano & Napoletano, Mauro & Schweitzer, Frank, 2012. "The efficiency and stability of R&D networks," Games and Economic Behavior, Elsevier, vol. 75(2), pages 694-713.
    9. repec:spo:wpecon:info:hdl:2441/9935 is not listed on IDEAS
    10. Réti, Tamás, 2019. "On some properties of graph irregularity indices with a particular regard to the σ-index," Applied Mathematics and Computation, Elsevier, vol. 344, pages 107-115.
    11. M. Koenig & Claudio J. Tessone & Yves Zenou, "undated". "A Dynamic Model of Network Formation with Strategic Interactions," Working Papers CCSS-09-006, ETH Zurich, Chair of Systems Design.
    12. repec:hal:wpspec:info:hdl:2441/7346 is not listed on IDEAS
    13. repec:hal:spmain:info:hdl:2441/7346 is not listed on IDEAS
    14. repec:spo:wpecon:info:hdl:2441/7346 is not listed on IDEAS
    15. Pierre Hansen & Nenad Mladenović & José Moreno Pérez, 2010. "Variable neighbourhood search: methods and applications," Annals of Operations Research, Springer, vol. 175(1), pages 367-407, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Maenhout, Broos & Vanhoucke, Mario, 2010. "A hybrid scatter search heuristic for personalized crew rostering in the airline industry," European Journal of Operational Research, Elsevier, vol. 206(1), pages 155-167, October.
    2. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2018. "Minimizing Piecewise-Concave Functions Over Polyhedra," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 580-597, May.
    3. Amina Lamghari & Roussos Dimitrakopoulos & Jacques Ferland, 2015. "A hybrid method based on linear programming and variable neighborhood descent for scheduling production in open-pit mines," Journal of Global Optimization, Springer, vol. 63(3), pages 555-582, November.
    4. Patricia Domínguez-Marín & Stefan Nickel & Pierre Hansen & Nenad Mladenović, 2005. "Heuristic Procedures for Solving the Discrete Ordered Median Problem," Annals of Operations Research, Springer, vol. 136(1), pages 145-173, April.
    5. Ali Shahabi & Sadigh Raissi & Kaveh Khalili-Damghani & Meysam Rafei, 2021. "Designing a resilient skip-stop schedule in rapid rail transit using a simulation-based optimization methodology," Operational Research, Springer, vol. 21(3), pages 1691-1721, September.
    6. Wilson, Duncan T. & Hawe, Glenn I. & Coates, Graham & Crouch, Roger S., 2013. "A multi-objective combinatorial model of casualty processing in major incident response," European Journal of Operational Research, Elsevier, vol. 230(3), pages 643-655.
    7. Felipe, Ángel & Ortuño, M. Teresa & Righini, Giovanni & Tirado, Gregorio, 2014. "A heuristic approach for the green vehicle routing problem with multiple technologies and partial recharges," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 71(C), pages 111-128.
    8. Fowler, John W. & Mönch, Lars, 2022. "A survey of scheduling with parallel batch (p-batch) processing," European Journal of Operational Research, Elsevier, vol. 298(1), pages 1-24.
    9. Véronique François & Yasemin Arda & Yves Crama, 2019. "Adaptive Large Neighborhood Search for Multitrip Vehicle Routing with Time Windows," Transportation Science, INFORMS, vol. 53(6), pages 1706-1730, November.
    10. Tino Henke & M. Grazia Speranza & Gerhard Wäscher, 2014. "The Multi-Compartment Vehicle Routing Problem with Flexible Compartment Sizes," FEMM Working Papers 140006, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    11. Timo Hintsch, 2019. "Large Multiple Neighborhood Search for the Soft-Clustered Vehicle-Routing Problem," Working Papers 1904, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    12. Olcay Polat & Can B. Kalayci & Özcan Mutlu & Surendra M. Gupta, 2016. "A two-phase variable neighbourhood search algorithm for assembly line worker assignment and balancing problem type-II: an industrial case study," International Journal of Production Research, Taylor & Francis Journals, vol. 54(3), pages 722-741, February.
    13. Janssens, Jochen & Van den Bergh, Joos & Sörensen, Kenneth & Cattrysse, Dirk, 2015. "Multi-objective microzone-based vehicle routing for courier companies: From tactical to operational planning," European Journal of Operational Research, Elsevier, vol. 242(1), pages 222-231.
    14. Jiang, Min & Huang, George Q., 2022. "Intralogistics synchronization in robotic forward-reserve warehouses for e-commerce last-mile delivery," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 158(C).
    15. Xiao, Yiyong & Kaku, Ikou & Zhao, Qiuhong & Zhang, Renqian, 2011. "A reduced variable neighborhood search algorithm for uncapacitated multilevel lot-sizing problems," European Journal of Operational Research, Elsevier, vol. 214(2), pages 223-231, October.
    16. Bani, Abderrahman & El Hallaoui, Issmail & Corréa, Ayoub Insa & Tahir, Adil, 2023. "Solving a real-world multi-depot multi-period petrol replenishment problem with complex loading constraints," European Journal of Operational Research, Elsevier, vol. 311(1), pages 154-172.
    17. Roe, R.A. & Smeelen, M. & Hoefeld, C., 2005. "Outsourcing and organizational change : an employee perspective," Research Memorandum 045, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    18. Bruglieri, Maurizio & Liberti, Leo, 2008. "Optimal running and planning of a biomass-based energy production process," Energy Policy, Elsevier, vol. 36(7), pages 2430-2438, July.
    19. Pan, Quan-Ke & Gao, Liang & Li, Xin-Yu & Gao, Kai-Zhou, 2017. "Effective metaheuristics for scheduling a hybrid flowshop with sequence-dependent setup times," Applied Mathematics and Computation, Elsevier, vol. 303(C), pages 89-112.
    20. Drezner, Zvi, 2005. "The extended concentric tabu for the quadratic assignment problem," European Journal of Operational Research, Elsevier, vol. 160(2), pages 416-422, January.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:191:y:2008:i:3:p:661-676. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.