Another class of balanced graph designs: balanced circuit designs

A block considered as a set of elements together with its adjacency matrix A is called a C-block if A is the adjacency matrix of a circuit. A balanced circuit design with parameters v, b, r, k, λ (briefly, BCD(v, k, λ)) is an arrangement of v elements into bC-blocks such that each C-block contains k elements, each element occurs in exactly rC-blocks and any two distinct elements are linked in exactly λ C-blocks.We investigate conditions for the existence of BCD and show, in particular, that if the block-size k ? 6 and the trivial necessary conditions are satisfied, then the corresponding BCD exists.     

Spectral and thermal studies of some 4-(O-acetyl)glycopyranosylaminopyrimidine derivatives

A spectral study (IR and UV spectroscopies) of seven 4-(O-acetyl)glycopyranosylaminopyrimidine derivatives has been carried out. The thermal study of the compounds allowed us to characterize the following processes: (i) desolvations, (ii) solid-solid transitions, (iii) melting, (iv) pyrolytic decompositions. Through the IR spectral study it was established that pyrolytic decompositions of all the compounds start with the acetyl groups. The reaction orders and activation energies of the deacetylation processes have been calculated.     

On hypohamiltonian graphs

Herz, Duby and Vigué [9] conjectured that every hypohamiltonian graph has girth 5. In the present note hypohamiltonian graphs of girth 3 and 4 are described. Also two conjectures on hypohamiltonian graphs made by Bondy and Chvátal, respectively, are disproved.