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An application of modified group divisible designs
Journal of Combinatorial Theory, Series A, 1994 Let \(\kappa\), \(\lambda\), \(m\), \(\upsilon\) be positive integers. A group divisible design of order \(\kappa\), \(\lambda\), \(m\), \(\upsilon\) consists of a finite set \(V\) of points, a partition \(\gamma= \{G_ 1,\dots, G_ r\}\) of \(V\) into \(r\) subsets of \(V\) called groups and a collection \(\beta= \{B_ 1, B_ 2,\dots\}\) consisting of ...
Assaf, Ahmed M
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Group divisible designs with block-size four [PDF]
Discrete Mathematics, 1977 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
A.E. Brouwer (Andries) +2 more
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Research on fractional repetition codes based on group divisible designs [PDF]
Tongxin xuebao, 2015 A novel design of FR (fractional repetition) codes was proposed which aims at providing efficient repair at the minimum bandwidth regenerating point.The design consisted of an outer MDS (maximum distance separable) code and an inner repetition code ...
Bing ZHU +4 more
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A new regular group divisible design
Examples and Counterexamples, 2021 A regular group divisible design with parameters: v=b=39, r=k=9, λ1=0, λ2=2, m=13, n=3is obtained using balanced generalized Weighing matrix over a dihedral group of order 6.
Shyam Saurabh, Kishore Sinha
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Existence of a new class of group divisible designs with block size four
Nantong Daxue xuebao. Ziran kexue ban, 2022 Group divisible designs are not only kinds of classical designs in combinatorial design theory, but also have extremely important applications in coding theory.
TANG Jiahao WANG Jinhua
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Genetic susceptibility to multiple sclerosis in African Americans
PLoS ONE, 2021 Objective To explore the nature of genetic-susceptibility to multiple sclerosis (MS) in African-Americans. Background Recently, the number of genetic-associations with MS has exploded although the MS-associations of specific haplotypes within the major ...
Douglas S. Goodin +4 more
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3-Group Divisible Designs with 3 Groups and Block Size 5
Journal of Mathematics, 2023 A 3-GDD (n, 2, k, λ1, λ2) was defined by combining the definitions of a group divisible design and a t-design. In this paper, we extend the definitions to 3 groups and block size 5, and we denote such GDD by 3-GDD (n, 3, 5, μ1, μ2).
Zebene Girma Tefera +2 more
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, 2010 A divisible design graph is a graph whose adjacency matrix is the incidence matrix of a divisible design. Divisible design graphs are a natural generalization of (v,k,λ)-graphs, and like (v,k,λ)-graphs they make a link between combinatorial design theory
Kharaghani, H. +12 more
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Designs for graphs with six vertices and ten edges
Electronic Journal of Graph Theory and Applications, 2019 The design spectrum has been determined for two of the 15 graphs with six vertices and ten edges. In this paper we completely solve the design spectrum problem for a further eight of these graphs.
A. D. Forbes, T. S. Griggs, K. A. Forbes
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On group divisible covering designs
Discrete Mathematics, 1999 The notion of group divisible covering design (GDCD) is introduced. The number of blocks in a minimum GDCD with block size \(k\) and group-type \(g^u\), is the covering number \( C(k,g^u)\), whose values are determined for all positive integers \(g\) and \(u\geq 3\).
Katherine Heinrich, Jianxing Yin
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