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Some properties of graph centroids

  • Section III Graph-Theoretical Aspects Of TND
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Abstract

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 andU ⊂V(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.

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Authors and Affiliations

  1. Institute of Computer Science, University of Wrocław, Przesmyckiego 20, 51151, Wrocław, Poland

    W. Piotrowski & M. M. Sysło

Authors
  1. W. Piotrowski
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  2. M. M. Sysło
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Additional information

This research has been partly supported by Grant RP.I.09 from the Institute of Computer Science, University of Warsaw. This paper was completed when the second author was at Fachbereich 3 -Mathematik, Technische Universität Berlin, supported also by the Alexander von Humboldt-Stiftung (Bonn).

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Piotrowski, W., Sysło, M.M. Some properties of graph centroids. Ann Oper Res 33, 227–236 (1991). https://doi.org/10.1007/BF02115757

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