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The paper deals with Hamiltonian and pancyclic graphs in the class of all self-centered graphs of radius 2. For both of the two considered classes of graphs we have done the following. For a given number n of vertices, we have found an upper bound of the minimum size of such graphs. For n ≤ 12 we have found the exact values of the minimum size. On the other hand, the exact value of the maximum size has been found for every n. Moreover, we have shown that such a graph (of order n and) of size m exists for every m between the minimum and the maximum size. For n ≤ 10 we have found all nonisomorphic graphs of the minimum size, and for n = 11 only for Hamiltonian graphs.

In the paper it is shown that every tree with diameter 5 is graceful.

Classical methods for the synthesis of indan-1,3-dione derivatives failed when applied to their tricarbonylchromium complexes. The desired 2-substituted (η6-indan-1,3-dione)tricarbonylchromium complexes were prepared starting from protected indan-1,3-dione derivatives such as bis(dioxolanes) and enol ethers. Tricarbonylchromium complexes of indan-1,3-dione having at least one hydrogen at C-2 are unstable. Nevertheless, ethylation of 2-methyl(η6-indan-1,3-dione)tricarbonylchromium and methylation of 2-ethyl(η6-indan-1,3-dione)tricarbonylchromium were possible and proceeded with high stereoselectivity.

A synthesis of new, chiral tricarbonyliron complexes (1, 2) from 1,3-cyclohexanedione and 5,5-dimethyl-1,3-cyclohexanedione (dimedone) after their conversion to 1,3-diacetoxy-1,3-cyclohexadienes and complexation with Fe2(CO)9 is described. Ligand-exchange reactions of complexes 1,2 with PPh3 (A), (−)-P(OHC)∗(Me)-COOEt)3 ‘(−)-TEOCEOP’ (B) and and (−)-PPh2(OHC∗(Me)-COOEt) ‘LACTODIPPHOS’ (C) were accomplished in good yield. A new prospective chiral ligand for organoiron chemistry, derived from commercially available (S)-(−)-ethyl lactate, (−)-PPh2(OHC∗(Me)-COOEt) (C) was found. By means of ligand C, a diastereoisomeric mixture of the (1,3-diacetoxy-1,3-cyclohexadiene)Fe(Co)2PPh2(OHC∗(Me)-COOet) complex 1C (IC120 and1C160) was successfully separated.

Reactions of 2-acyl-1,3-indandiones with nitrogen nucleophiles were studied rarely. The question, if they react with carbonyl carbon of acyl group or indandione skeleton, has not been answered unambiguously. To make clear the question which carbonyl carbon of 2-acyl-1,3-indandiones enters the reaction with nitrogen nucleophiles we carried out the reactions with 2-acetyl- (Ia), 2-propionyl- (Ib), 2-pivaloyl- (Ic), and 2-benzoyl-1,3-indandione (Id). We used different 2-acyl-1,3-indandiones with the aim to find out if the character of acyl group affects the course of reaction. We used ethoxyamine, primary amines, phenylhydrazine, hydrazine and methylhydrazine as nucleophile reactants. The reactions were carried out in methanol at reflux at 10% excess of nitrogen base. The reactions with phenylhydrazine, hydrazine and methylhydrazine were performed with twofold excess of nitrogen base. The separation of reaction products was carried out by chromatography on silica gel. We found that 2-acyl-1,3-indandiones I react with ethoxyamine both at the acylcarbonyl carbon to produce 2-(1-ethoxyiminoalkyl)-1,3-indandiones II and the carbonyl carbon of indandione skeleton to give rise 3-(ethoxyimino)-2-acyl-1-indanones III. In all cases, the carbonyl carbon of acyl group was preferred (the observed ratio of products II to III was 6 - 8 : 1). From the reaction of 2-acyl-1,3-indandiones with primary amines only the products IV of reaction with the acylcarbonyl carbon were isolated. The hydrazines used reacted with 2-acyl-1,3-indandiones also at carbonyl carbon of acyl group in the first step to produce hydrazones. However, the products isolated in most cases were formed by the attack of hydrazone nitrogen at carbonyl carbon of indandione skeleton giving rise to derivatives of indeno[2,3-d]pyrazole-4-one V. It is interesting that 2-acetyl-1,3-indandione and 2-propionyl-1,3-indandione, reacting with phenylhydrazine and hydrazine, yielded only corresponding hydrazones VI.

An efficient method for preparing 1,3-diacetoxy-1,3-cyclo-alkadienes 2a-e, from 1,3-cycloalkanediones 1a-e by treatment with ketene in the presence of p-toluenesulfonic acid is described

A new efficient method for preparation of acyclic α-acetylated β-diketone copper(II) chelates and their corresponding geminal triketones by treatment of starting β-diketone cuprates (1) with ketene is described

Reactions of 2-acyl-1,3-indandiones with nitrogen nucleophiles were studied rarely. The question, if they react with carbonyl carbon of acyl group or indandione skeleton, has not been answered unambiguously. To make clear the question which carbonyl carbon of 2-acyl-1,3-indandiones enters the reaction with nitrogen nucleophiles we carried out the reactions with 2-acetyl- ( Ia ), 2-propionyl- ( Ib ), 2-pivaloyl- ( Ic ), and 2-benzoyl-1,3-indandione ( Id ). We used different 2-acyl-1,3-indandiones with the aim to find out if the character of acyl group affects the course of reaction. We used ethoxyamine, primary amines, phenylhydrazine, hydrazine and methylhydrazine as nucleophile reactants. The reactions were carried out in methanol at reflux at 10% excess of nitrogen base. The reactions with phenylhydrazine, hydrazine and methylhydrazine were performed with twofold excess of nitrogen base. The separation of reaction products was carried out by chromatography on silica gel. We found that 2-acyl-1,3-indandiones I react with ethoxyamine both at the acylcarbonyl carbon to produce 2-(1-ethoxyiminoalkyl)-1,3-indandiones II and the carbonyl carbon of indandione skeleton to give rise 3-(ethoxyimino)-2-acyl-1-indanones III . In all cases, the carbonyl carbon of acyl group was preferred (the observed ratio of products II to III was 6 - 8 : 1). From the reaction of 2-acyl-1,3-indandiones with primary amines only the products IV of reaction with the acylcarbonyl carbon were isolated. The hydrazines used reacted with 2-acyl-1,3-indandiones also at carbonyl carbon of acyl group in the first step to produce hydrazones. However, the products isolated in most cases were formed by the attack of hydrazone nitrogen at carbonyl carbon of indandione skeleton giving rise to derivatives of indeno[2,3- d ]pyrazole-4-one V . It is interesting that 2-acetyl-1,3-indandione and 2-propionyl-1,3-indandione, reacting with phenylhydrazine and hydrazine, yielded only corresponding hydrazones VI .

Acetylation of lower 1,3-cycloalkenediones with ketene takes place exclusively at oxygen in contrast to acyclic β-diketones. Thus, 1,3-cyclopentanedione (I), 1,3-cyclohexanedione (II) and 5,5-dimethyl-1,3-cyclohexanedione (III) afforded the corresponding 3-acetoxy-2-cycloalken-1-ones VI - VIII in quantitative yields. 1,3-Cycloheptanedione (IV) and 1,3-cyclooctanedione (V) differed considerably from the preceding diketones by low reactivities.

3-Acyloxy-5-(2-phenylethenyl)-2-cyclohexen-1-ones II were prepared by O-acylation of 5-(2-phenylethenyl)-1,3-cycloxanedione (I). Treatment of II with AlCl3 resulted in rearrangement of the acyl group to the double bond of the phenylethenyl grouping followed by cyclization to 8-acyl-7-phenylbicyclo[2.2.2]octane-2,6-diones III. Their structure was evidenced by analysis of the 1H and 13C NMR spectral data.

3-Acyloxy-5-(2-phenylethenenyl)-2-cyclohexen-1-ones (I) were prepared by O-acylation of 5-(2-phenylethenenyl)-1,3-cycloxanedione. Treatment of I with AlCl 3 resulted in rearrangement of the acyl group to the double bond of the phenylethenyl grouping followed by cyclization to 8-acyl-7-phenylbicyclo[2.2.2]octane-2,6-diones. Their structure was evidenced by analysis of the 1 H and 13 C NMR spectral data

A new efficient method for preparation of acyclic α-acetylated β-diketone copper(II) chelates and their corresponding geminal triketones by treatment of starting β-diketone cuprates (1) with ketene is described

An efficient method for preparing 1,3-diacetoxy-1,3-cyclo-alkadienes 2a-e, from 1,3-cycloalkanediones 1a-e by treatment with ketene in the presence of p-toluenesulfonic acid is described

Kinetics of alkaline hydrolysis of mono- and dimethyl esters of 2,3- and 3,4-thiophenedicarboxylic acids and their dihydroanalogues have been studied in 70% dioxane. The rate measurements have been carried out by the titrimetric method and the k1, k2 rate constants evaluated by the Frost-Schwemer method. The activation parameters of these reactions have been calculated. The results are compared with kinetic parameters of alkaline hydrolysis of methyl and dimethyl phthalates. The hydrolysis rate is significantly affected by the cyclic system to which the methoxycarbonyl groups are bound, the reactivity order being: Dihydrothiophene > thiophene > benzene. Also measured were the kinetics of alkaline hydrolyses of methyl 4-cyano-3-thiophenecarboxylate and 3-cyano-2-thiophenecarboxylate and of their dihydroanalogues. No meaningful preference of the hydrolysis of the group at the position 2 has been observed in case of 2,3-isomers. However, it has been confirmed that the hyper- and hypo-ortho transfer of electronic effects operates in the thiophene nucleus.

The photochemical isomerizations have been studied of 2-phenyl-1,3-indanedione to mixture of E- and Z-benzalphthalide and of E-benzalphthalide to Z-benzalphthalide depending on the solvent used, concentration, and the light wavelength. The attempts at the reverse photochemical isomerization of E-benzalphthalide to 2-phenyl-1,3-indanedione have failed. Quantum yields of the isomerization of 2-phenyl-1,3-indanedione decrease in the following solvent series: cyclohexane acetonitrile benzene tetrachlormethane methanol. The isomerization quantum yield of 2-phenyl01,3-indanedione is inversely proportional to concentration of the starting substance, but the dependence of 1/φ on the concentration is not linear.

13C and 29Si NMR chemical shifts are reported for several 1-trimethylsiloxycycloalkenes and 1,2-bis(trimethylsiloxy)cycloalkenes, (CH3)3SiO)xCnH2n-2-x (x = 1,2), dissolved in hexadeuterioacetone. Several correlations of the chemical shifts with structural parameters (ring size, interatomic distances etc.) are noted and an attempt is made to explain the found strong dependence of the 29Si chemical shifts on the ring size. Steric crowding with the nearest CH2 group drives the trimethylsilyl group out of the double bond plane and thus causes steric inhibition of the resonance of unshered oxygen electron pairs with electrons of the double bond. Since the crowding becomes more accute with increasing ring size, the ring size is in this way projected into the chemical shifts of silicon and olefinic carbons. This mechanism provides a united interpretation of all observed NMR chemical shifts.

Michael addition of 1,3-cyclopentanedione, 1,3-cyclohexanedione and 1,3-cycloheptanedione to 1-(X-phenyl)-2-nitroethylenes was studied. 1,3-Cyclopentanedione afforded 2-(1-(X-phenyl)-2-nitroethyl)-1,3-cyclopentanediones (I), 1,3-cyclohexanedione gave 9-(X-phenyl)-8-hydroxyimino-7-oxabicyclo[4,3,0]-1-nonen-2-ones (IIa-IIe),whereas reaction with 1,3-cycloheptanedione led to 10-(X-phenyl)-8-oxabicyclo[5,3,0]-1-decen-2-ones (IIg-IIj) as well as 9,9'-hydroxyaminobis(10-(X-phenyl)-8-oxabicyclo[5,3,0]-1-decen-2-ones) (III). Products I were isolated also in the addition of 1,3-cyclohexadione and 1,3-cycloheptanedione to 1-(X-phenyl)-2-nitroethylene when X=H or an electron accepting substituent and the reaction was performed at -5 to 0°C, and were converted into II. The structure of the compounds and mechanism of the conversion of I to II is discussed on the basis of IR, 1H NMR and 13C NMR spectra.