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41.
A divisible design graph (DDG for short) is a graph whose adjacency matrix is the incidence matrix of a divisible design. DDGs were introduced by Kharaghani, Meulenberg and the second author as a generalization of $(v,k,\lambda )$ -graphs. It turns out that most (but not all) of the known examples of DDGs are walk-regular. In this paper we present an easy criterion for this to happen. In several cases walk-regularity is forced by the parameters of the DDG; then known conditions for walk-regularity lead to nonexistence results for DDGs. In addition, we construct some new DDGs, and check old and new constructions for walk-regularity. In doing so, we present and use special properties in case the classes have size two. All feasible parameter sets for DDGs on at most $27$ vertices are examined. Existence is established in all but one case, and existence of a walk-regular DDG in all cases.  相似文献   
42.
A series of 2-substituted-7-alkyl-4,7-dihydro-4-oxothiazolo[5,4-b]pyridine-5-carboxylic acids were synthesized. Antibacterial activity was tested in vitro. None of the new compounds prepared showed any antibacterial activity in vitro against the strains tested.  相似文献   
43.
In this paper we examine 2-designs having an intersection number k ? n. This intersection number gives rise to an equivalence relation on the blocks of the design. Conditions on the sizes of these equivalence classes and some properties of any further intersection numbers are obtained. If such a design has at most three intersection numbers then it gives rise to a strongly regular graph. This leads to a result on the embedding of quasi-residual designs. As as example a quasi-residual 2-(56, 12, 3) design is constructed and embedded in a symmetric 2-(71, 15, 3) design.  相似文献   
44.
A series of 7-(2-substituted-4-thiazolyl and thiazolidinyl)-1-ethyl-1,4-dihydro-4-oxoquinoline-3-carboxylic acids and their 6-fluoro analogues were synthesized. The Hantzsch method was used for the preparation of the thiazolylquinolones. The thiazolidinylquinolones were synthesized by quaternization of the corresponding thiazolyl analogues, followed by reduction of the obtained thiazolium salts with sodium borohydride in aqueous solution. Antibacterial activity was tested in vitro. Most of the compounds were inactive against Gram-negative bacteria but some of them showed however good activity against Gram-positive bacteria and mycobacteria. This activity pattern is rarely found among the quinolone antibacterials.  相似文献   
45.
6-Substituted benzyl-4-phenyl-3-thioxo-2,3,4,5-tetrahydro-1,2,4-triazin-5-ones 3a-d were prepared and converted into their corresponding 3-methylthio derivatives 4a-d . Reaction of compounds 4a-d with hydrazine hydrate gave the corresponding 4-amino-3-anilino-4,5-dihydro-1,2,4-triazin-5-ones 5a-d . 6-Substituted benzyl-4-phenyl-2,3,4,5-tetrahydro-1,2,4-triazin-3,5-diones 9a-c were synthesized and allowed to react with hydrazine hydrate to give the corresponding 6-substituted benzyl-4-amino-2,3,4,5-tetrahydro-1,2,4-triazin-3,5-diones 10a-c . The biological evaluation of some of these triazines is described. All compounds were screened for antiviral, antibacterial, antimycobacterial, antifungal and antiyeast activity. No important biological activity was found.  相似文献   
46.
We consider the following generalization of strongly regular graphs. A graph G is a Deza graph if it is regular and the number of common neighbors of two distinct vertices takes on one of two values (not necessarily depending on the adjacency of the two vertices). We introduce several ways to construct Deza graphs, and develop some basic theory. We also list all diameter two Deza graphs which are not strongly regular and have at most 13 vertices.  相似文献   
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48.
Designs, Codes and Cryptography - A conference matrix of order n is an $$n\times n$$ matrix C with diagonal entries 0 and off-diagonal entries $$\pm 1$$ satisfying $$CC^\top =(n-1)I$$ . If C is...  相似文献   
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50.
We show that there is a unique graph with spectrum as in the title. It is a subgraph of the McLaughlin graph. The proof uses a strong form of the eigenvalue interlacing theorem to reduce the problem to one about root lattices.  相似文献   
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