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Equipartite graphs

Israel Journal of Mathematics volume 168, pages 431–444 (2008)Cite this article

Abstract

A graph G of even order is weakly equipartite if for any partition of its vertex set into subsets V 1 and V 2 of equal size the induced subgraphs G[V 1] and G[V 2] are isomorphic. A complete characterization of (weakly) equipartite graphs is derived. In particular, we show that each such graph is vertex-transitive. In a subsequent paper, we use these results to characterize equipartite polytopes, a geometric analogue of equipartite graphs.

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Author information

Affiliations

  1. Department of Mathematics, University of Washington, Seattle, WA, 98195, USA

    Branko Grünbaum

  2. Department of Mathematics, University of West Bohemia, Univerzitní 8, 306 14, Plzeň, Czech Republic

    Tomáš Kaiser

  3. Institute for Theoretical Computer Science (ITI), Charles University, Prague, Czech Republic

    Tomáš Kaiser & Daniel Král’

  4. Department of Applied Mathematics, Charles University, Malostranské nám. 25, 118 00, Prague 1, Czech Republic

    Daniel Král’

  5. Computing and Software Systems Program, University of Washington, Tacoma, WA, 98402, USA

    Moshe Rosenfeld

Authors
  1. Branko Grünbaum
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  2. Tomáš Kaiser
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  3. Daniel Král’
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  4. Moshe Rosenfeld
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Corresponding author

Correspondence to Branko Grünbaum.

Additional information

Supported by Research Plan MSM 4977751301 of the Czech Ministry of Education. The Institute for Theoretical Computer Science is supported by Czech Ministry of Education as projects LN00A056 and 1M0545.

Support by the Fulbright Senior Specialist Program for his stay in Pilsen in summer 2003 is acknowleged.

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Grünbaum, B., Kaiser, T., Král’, D. et al. Equipartite graphs. Isr. J. Math. 168, 431–444 (2008). https://doi.org/10.1007/s11856-008-1071-5

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Keywords

  • Complete Graph
  • Regular Graph
  • Permutation Group
  • Common Neighbor
  • Nonadjacent Vertex