Locally Balanced G-Designs

Bonacini, Paola; Gionfriddo, Mario; Marino, Lucia

doi:10.3390/math11020408

Open AccessArticle

Locally Balanced G-Designs

by

Paola Bonacini

^*,†

,

Mario Gionfriddo

^† and

Lucia Marino

^†

Dipartimento di Matematica e Informatica, Università di Catania, 95125 Catania, Italy

^*

Author to whom correspondence should be addressed.

^†

These authors contributed equally to this work.

Mathematics 2023, 11(2), 408; https://doi.org/10.3390/math11020408

Submission received: 14 November 2022 / Revised: 26 December 2022 / Accepted: 6 January 2023 / Published: 12 January 2023

(This article belongs to the Special Issue Advances in Design Theory, Combinatorial Algebraic Geometry and Applications)

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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.

Keywords: G-designs; balanced; spectrum

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MDPI and ACS Style

Bonacini, P.; Gionfriddo, M.; Marino, L. Locally Balanced G-Designs. Mathematics 2023, 11, 408. https://doi.org/10.3390/math11020408

AMA Style

Bonacini P, Gionfriddo M, Marino L. Locally Balanced G-Designs. Mathematics. 2023; 11(2):408. https://doi.org/10.3390/math11020408

Chicago/Turabian Style

Bonacini, Paola, Mario Gionfriddo, and Lucia Marino. 2023. "Locally Balanced G-Designs" Mathematics 11, no. 2: 408. https://doi.org/10.3390/math11020408

APA Style

Bonacini, P., Gionfriddo, M., & Marino, L. (2023). Locally Balanced G-Designs. Mathematics, 11(2), 408. https://doi.org/10.3390/math11020408

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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