Annals of Operations Research

, Volume 33, Issue 3, pp 227–236 | Cite as

Some properties of graph centroids

  • W. Piotrowski
  • M. M. Sysło
Section III Graph-Theoretical Aspects Of TND


The concept of a branch weight centroid has been extended in [12] so that it can be defined for an arbitrary finite setX with a distinguished familyC of "convex" subsets ofX. In particular, the centroid of a graphG was defined forX to be the vertex setV(G) ofG andUV(G) is convex if it is the vertex set of a chordless path inG. In this paper, which is an extended version of [13], we give necessary and sufficient conditions for a graph to be a centroid of another graph as well as of itself. Then, we apply these results to some particular classes of graphs: chordal, Halin, series-parallel and outerplanar.


Extended Version Weight Centroid Chordless Path Branch Weight Finite setX 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    G.A. Dirac, On rigid circuit graphs, Abh. Math. Seminar Univ. Hamburg 25(1961)71–76.Google Scholar
  2. [2]
    M. Faber and R.E. Jamison, Convexity in graphs and hypergraphs, SIAM J. Alg. Discr. Math. 7(1986)433–444.Google Scholar
  3. [3]
    F. Gavril, Algorithms on clique separable graphs, Discr. Math. 19(1977)159–165.Google Scholar
  4. [4]
    M.C. Golumbic,Algorithmic Graph Theory and Perfect Graphs (Academic Press, New York, 1980).Google Scholar
  5. [5]
    R.E. Jamison-Waldner, A perspective on abstract convexity: Classifying alignments by varieties, in:Convexity and Related Combinatorial Geometry, ed. D.C. Kay and B. Drech (Dekker, New York, 1982)113–150.Google Scholar
  6. [6]
    R.E. Jamison-Waldner, Copoints in antimatroids, Congr. Numer. 29(1980)535–544.Google Scholar
  7. [7]
    R.E. Jamison-Waldner and P.H. Edelman, The theory of convex geometries, Geom. Dedicata 19(1985)247–270.Google Scholar
  8. [8]
    R.E. Jamison-Waldner and R. Nowakowski, A Helly theorem for convexity in graphs, Discr. Math. 51(1984)35–39.Google Scholar
  9. [9]
    C. Jordan, Sur les assemblages de lignes, J. reine und angew. Math. 70(1869)185–190.Google Scholar
  10. [10]
    G. Kothe,Topologische Lineare Räume I (Springer, Berlin, 1960).Google Scholar
  11. [11]
    O. Ore,Theory of Graphs (AMS, Providence, RI, 1962).Google Scholar
  12. [12]
    W. Piotrowski, A generalization of branch weight centroids, Zastosow. Matem. 19(1987)541–545.Google Scholar
  13. [13]
    W. Piotrowski and M.M. Sysło, A characterization of centroidal graphs, in:Combinatorial Optimization, Lecture Notes in Mathematics, Vol. 1403, ed. B. Simeone (Springer, Berlin, 1989), pp. 272–281.Google Scholar
  14. [14]
    P.J. Slater, Maximin facility location, J. Res. Nat. Bur. Standards B79(1975)107–115.Google Scholar
  15. [15]
    P.J. Slater, Accretion centers: A generalization of branch weight centroids, Discr. Appl. Math. 3(1984)187–192.Google Scholar
  16. [16]
    R.E. Tarjan, Decomposition by clique separators, Discr. Math. 55(1985)221–232.Google Scholar
  17. [17]
    B. Zelinka, A remark on self-centroidal graphs, to appear.Google Scholar

Copyright information

© J.C. Baltzer AG, Scientific Publishing Company 1991

Authors and Affiliations

  • W. Piotrowski
    • 1
  • M. M. Sysło
    • 1
  1. 1.Institute of Computer ScienceUniversity of WrocławWrocławPoland

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