Block-Graceful Designs
نویسندگان
چکیده
In this article, we adapt the edge-graceful graph labeling definition into block designs and define a design V , B with id="M2"> open="|" close="|" = v id="M3"> b as block-graceful if there exists bijection id="M4"> f : ⟶ open="{" close="}" 1,2 … such that induced mapping id="M5"> + Z given by id="M6"> x ∑ ∈ A mathvariant="normal">mod is bijection. A quick observation shows every id="M7"> r k λ − BIBD generated from cyclic difference family when id="M8"> 1 . As immediate consequences of observation, can obtain Steiner triple system order id="M9"> for all id="M10"> ≡ 6 projective geometries, i.e., id="M11"> q d / BIBDs. give necessary condition prove some basic results on existence id="M12"> We consider case id="M13"> 3 systems recursive construction obtaining those smaller which allows us to get infinite families id="M14"> id="M15"> also affine geometries integer id="M16"> ≥ 2 id="M17"> , where id="M18"> an odd prime power or id="M19"> 4 id="M20"> BIBD. make list small parameters problem labelings completely solved pairwise nonisomorphic BIBDs these parameters. complete article open problems conjectures.
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ژورنال
عنوان ژورنال: Journal of Mathematics
سال: 2023
ISSN: ['2314-4785', '2314-4629']
DOI: https://doi.org/10.1155/2023/4959576