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Axiomatic Characterization of the Median Function of a Block Graph

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Algorithms and Discrete Applied Mathematics (CALDAM 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12601))

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Abstract

A median of a profile of vertices (a sequence of vertices) on a connected graph is a vertex that minimizes the sum of the distances to the elements in the profile. The median function has as output the set of medians of a profile. Median function is an important consensus function for the location of a desirable facility in a network. The axiomatic characterization of the median function is studied by several authors on special classes of graphs like trees and median graphs. In this paper, we determine the median sets of all types of profiles and obtain an axiomatic characterization for the median function on block graphs, an immediate generalization of trees.

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References

  1. Arrow, K.J.: Social Choice and Individual Values, vol. 12. Yale University Press, London (2012)

    MATH  Google Scholar 

  2. Balakrishnan, K., Changat, M., Mulder, H.M.: The plurality strategy on graphs. Australas. J. Comb. 46, 191–202 (2010)

    MathSciNet  MATH  Google Scholar 

  3. Bandelt, H.J., Chepoi, V.: Graphs with connected medians. SIAM J. Discrete Math. 15(2), 268–282 (2002)

    Article  MathSciNet  Google Scholar 

  4. Bandelt, H.J., Mulder, H.M., Wilkeit, E.: Quasi-median graphs and algebras. J. Graph Theory 18(7), 681–703 (1994)

    Article  MathSciNet  Google Scholar 

  5. Changat, M., Lekha, D.S., Mohandas, S., Mulder, H.M., Subhamathi, A.R.: Axiomatic characterization of the median and antimedian function on a complete graph minus a matching. Discrete Appl. Math. 228, 50–59 (2017)

    Article  MathSciNet  Google Scholar 

  6. Hagauer, J.: Skeletons, recognition algorithm and distance matrix of quasi-median graphs. Int. J. Comput. Math. 55(3–4), 155–171 (1995)

    Article  Google Scholar 

  7. Holzman, R.: An axiomatic approach to location on networks. Math. Oper. Res. 15(3), 553–563 (1990)

    Article  MathSciNet  Google Scholar 

  8. Kemeny, J.G., Snell, L.: Preference ranking: an axiomatic approach. Math. Models Soc. Sci. 9–23 (1962)

    Google Scholar 

  9. Klavzar, S., Mulder, H.M.: Median graphs: characterizations, location theory and related structures. J. Comb. Math. Comb. Comput. 30, 103–128 (1999)

    MathSciNet  MATH  Google Scholar 

  10. McMorris, F., Neumann, D.: Consensus functions defined on trees. Math. Soc. Sci. 4(2), 131–136 (1983)

    Article  MathSciNet  Google Scholar 

  11. McMorris, F.R., Mulder, H.M., Ortega, O.: Axiomatic characterization of the mean function on trees. Discrete Math. Algorithms Appl. 2(03), 313–329 (2010)

    Article  MathSciNet  Google Scholar 

  12. McMorris, F.R., Mulder, H.M., Ortega, O.: The \(\ell _p\)-function on trees. Networks 60(2), 94–102 (2012)

    Article  MathSciNet  Google Scholar 

  13. McMorris, F.R., Mulder, H.M., Roberts, F.S.: The median procedure on median graphs. Discrete Appl. Math. 84(1–3), 165–181 (1998)

    Article  MathSciNet  Google Scholar 

  14. McMorris, F.R., Mulder, H.M., Vohra, R.V.: Axiomatic characterization of location functions. In: Advances in Interdisciplinary Applied Discrete Mathematics, pp. 71–91. World Scientific (2011)

    Google Scholar 

  15. McMorris, F.R., Roberts, F.S., Wang, C.: The center function on trees. Netw.: Int. J. 38(2), 84–87 (2001)

    Article  MathSciNet  Google Scholar 

  16. Mulder, H.M.: The majority strategy on graphs. Discrete Appl. Math. 80(1), 97–105 (1997)

    Article  MathSciNet  Google Scholar 

  17. Mulder, H.M.: Median graphs.: a structure theory. In: Advances in Interdisciplinary Applied Discrete Mathematics, pp. 93–125. World Scientific (2011)

    Google Scholar 

  18. Mulder, H.M., Novick, B.: An axiomatization of the median procedure on the n-cube. Discrete Appl. Math. 159(9), 939–944 (2011)

    Article  MathSciNet  Google Scholar 

  19. Mulder, H.M., Novick, B.: A tight axiomatization of the median procedure on median graphs. Discrete Appl. Math. 161(6), 838–846 (2013)

    Article  MathSciNet  Google Scholar 

  20. Mulder, H.M., Pelsmajer, M.J., Reid, K.: Axiomization of the center function on trees. Australas. J. Comb. 41, 223–226 (2008)

    MathSciNet  MATH  Google Scholar 

  21. Mulder, H.: The interval function of a graph, math. Centre Tracts 132 (1980)

    Google Scholar 

  22. Vohra, R.: An axiomatic characterization of some locations in trees. Eur. J. Oper. Res. 90(1), 78–84 (1996)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Futures Studies, University of Kerala, Thiruvananthapuram, 695581, India

    Manoj Changat & Nella Jeena Jacob

  2. Department of Mathematics, Government College Chittur, Palakkad, India

    Prasanth G. Narasimha-Shenoi

Authors
  1. Manoj Changat
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  2. Nella Jeena Jacob
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  3. Prasanth G. Narasimha-Shenoi
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Corresponding author

Correspondence to Manoj Changat .

Editor information

Editors and Affiliations

  1. Indian Institute of Technology Ropar, Rupnagar, India

    Apurva Mudgal

  2. Institute of Mathematical Sciences, Chennai, India

    C. R. Subramanian

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Changat, M., Jacob, N.J., Narasimha-Shenoi, P.G. (2021). Axiomatic Characterization of the Median Function of a Block Graph. In: Mudgal, A., Subramanian, C.R. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2021. Lecture Notes in Computer Science(), vol 12601. Springer, Cham. https://doi.org/10.1007/978-3-030-67899-9_24

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  • DOI: https://doi.org/10.1007/978-3-030-67899-9_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-67898-2

  • Online ISBN: 978-3-030-67899-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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