Novel trends in the chemistry of acridines. New fluorescent bioreagents and synthons on the basis of 9-isothiocyanatoacridines

9-Isothiocyanatoacridines containing a reactive NCS group, together with a biologically active acridine skeleton, were used for the synthesis of new acridine heterocycles. Their reactivity with aliphatic and aromatic amines as well as 15 amino acids was quantified by kinetic measurements. Sodium D-alkyl-N-(9-acridinyl)iminothiocarbonates obtained by addition of sodium alkoxides to the title compounds gave three types of products with organic halogen reagents. The reaction of above iminothiocarbonates with alkyl halides led to the fluorescent S-alkyl derivatives, whereas bromoacetyl bromide and alkyl bromoacetates afforded the 3-(9acridinyl)-1, 3-thiazolidine-2,4-diones and a new heterocycle, spiro[dihydroacridine-9(IOH), 4'-thiazoline], respectively.Department of Organic Chemistry, P. J. Safarik University, 04167 Kosice, Slovak Republic. Published in Khimiya Geterotsiklicheskikh Soedinenii, No. 10, pp. 1376–1379, October, 1995. Original article submitted July 1, 1995     

On automorphism groups of Cayley graphs

LetX _G,H denote the Cayley graph of a finite groupG with respect to a subsetH. It is well-known that its automorphism groupA(X_G,H) must contain the regular subgroupL _G corresponding to the set of left multiplications by elements ofG. This paper is concerned with minimizing the index [A(X_G,H)L_G] for givenG, in particular when this index is always greater than 1. IfG is abelian but not one of seven exceptional groups, then a Cayley graph ofG exists for which this index is at most 2. Nearly complete results for the generalized dicyclic groups are also obtained.     

Embedding graphs in Cayley graphs

IfY is a finite graph then it is known that every sufficiently large groupG has a Cayley graph containing an induced subgraph isomorphic toY. This raises the question as to what is sufficiently large. Babai and Sós have used a probabilistic argument to show that |G| > 9.5 |Y|³ suffices. Using a form of greedy algorithm we strengthen this to (2 + \sqrt 3 )|Y|^3 $$ " align="middle" border="0"> . Some related results on finite and infinite groups are included.     

Cancellation properties of products of graphs

This note extends results of Fernández, Leighton, and López-Presa on the uniqueness of rth roots for disconnected graphs with respect to the Cartesian product to other products and shows that their methods also imply new cancelation laws.     

On k-planar crossing numbers

The k-planar crossing number of a graph is the minimum number of crossings of its edges over all possible drawings of the graph in k planes. We propose algorithms and methods for k-planar drawings of general graphs together with lower bound techniques. We give exact results for the k-planar crossing number of K_2k+1,q, for k?2. We prove tight bounds for complete graphs. We also study the rectilinear k-planar crossing number.     

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