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Locally Balanced G-Designs

Author

Listed:
  • Paola Bonacini

    (Dipartimento di Matematica e Informatica, Università di Catania, 95125 Catania, Italy
    These authors contributed equally to this work.)

  • Mario Gionfriddo

    (Dipartimento di Matematica e Informatica, Università di Catania, 95125 Catania, Italy
    These authors contributed equally to this work.)

  • Lucia Marino

    (Dipartimento di Matematica e Informatica, Università di Catania, 95125 Catania, Italy
    These authors contributed equally to this work.)

Abstract

Let G be a graph and let K n be the complete graph of order n . A G -design is a decomposition of the set of edges of K n in graphs isomorphic to G , which are called blocks . It is well-known that a G -design is balanced if all the vertices are contained in the number of blocks of G . In this paper, the definition of locally balanced G-design is given, generalizing the existing concepts related to balanced designs. Further, locally balanced G-designs are studied in the cases in which G ≅ C 4 + e and G ≅ C 4 + P 3 , determining the spectrum.

Suggested Citation

  • Paola Bonacini & Mario Gionfriddo & Lucia Marino, 2023. "Locally Balanced G-Designs," Mathematics, MDPI, vol. 11(2), pages 1-8, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:408-:d:1033939
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    Keywords

    G-designs; balanced; spectrum;
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