In this paper, we continue to investigate the spectrum for {4}-GDDs of type gum1 with small
g. We show that, for each g∈{2, 4, 5, 12, 15} and each admissible pair (u, m), a {4}-GDD of …

Non-uniform group divisible designs have been studied by numerous researchers in the
past two decades due to their vital applications in the constructions for other types of …

SONET/WDM networks using wavelength add-drop multiplexing can be constructed using
certain graph decompositions used to form a grooming, consisting of unions of primitive …

Building upon the work of Wei and Ge (Designs, Codes, and Cryptography 74, 2015), we
extend the range of positive integer parameters g, u, and m for which group divisible designs …

The existence of HGDDs with block size four and its application to double frames -
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In this paper we discuss the existence problem for a semi-cyclic holey group divisible design
of type (n, m^ t)(n, mt) with block size 3 3, which is denoted by a 3 3-SCHGDD of type (n, m …

We determine, up to some possible exceptions, the spectrum for 4-GDDs of type gum1,
where g is a multiple of 8 until 48, g is a multiple of 24 until 144, respectively. These spectra …

We deal with group divisible designs (GDDs) that have block size four and group type gum
1, where g≡ 2 or 4 (mod 6). We show that the necessary conditions for the existence of a 4 …

In order to reduce the number of add-drop multiplexers (ADMs) in SONET/WDM networks
using wavelength add-drop multiplexing, certain graph decompositions can be used to form …

We show that the necessary conditions for the existence of group divisible designs with
block size four (4‐GDDs) of type are sufficient for (mod),= 39, 51, 57, 69, 87, 93, 111, 123 …