A note on the domination dot-critical graphs

A graph G is dot-critical if contracting any edge decreases the domination number. Nader Jafari Rad (2009) [3] posed the problem: Is it true that a connected k-dot-critical graph G with G^′=0? is 2-connected? In this note, we give a family of 1-connected 2k-dot-critical graph with G^′=0? and show that this problem has a negative answer.     

Growth of Co clusters on thin films Al2O3NiAl(100)

We present a scanning tunnel microscopy study of Co clusters grown through vapor deposition on Al(2)O(3) thin films over NiAl(100) at different coverages and temperatures. Formation of Co clusters was observed at 90, 300, 450, and 570 K. At the three lower temperatures, we find narrow cluster size distributions and the mean sizes (with a diameter of 2.6 nm and a height of 0.7 nm) do not change significantly with the coverage and temperature, until the clusters start to coalesce. Even on 3-4-nm-wide crystalline Al(2)O(3) strips where the deposited Co atoms are confined, the same features sustain. Only at 570 K the normal growth mode where the cluster size increases with the deposition coverage is observed, although the data are less conclusive. A simple modeling of kinetic surface processes on a strip confirms the normal growth mode, but fails to show a favored size unless additional energetic constraints are applied on the cluster sizes. Increasing Co coverages to cluster coalescence, a larger preferable size (mean diameter of 3.5 nm and height of 1.4 nm) appears for growth at 450 K. These two sizes are corroborated by morphology evolution of high Co coverages deposited at 300 K and annealed to 750 K, in which the coalescence is eliminated and the two preferable geometries appear and coexist.     

Forcing matching numbers of fullerene graphs

The forcing number or the degree of freedom of a perfect matching M of a graph G is the cardinality of the smallest subset of M that is contained in no other perfect matchings of G. In this paper we show that the forcing numbers of perfect matchings in a fullerene graph are not less than 3 by applying the 2-extendability and cyclic edge-connectivity 5 of fullerene graphs obtained recently, and Kotzig’s classical result about unique perfect matching as well. This lower bound can be achieved by infinitely many fullerene graphs.     

Organotransition-Metal Complexes of Multidentate Ligands 5. Structural Characterization of Cis-Tetracarbonyl(3,5-Dimethylpyrazol-1-Yl) Methanemolybdenum(0)

The title compound crystallizes in space group P 2₁/c of the monoclinic system in a cell of dimensions: a = 9.231(2), b = 15.931(2), c = 12.420(2) Å, β = 108.37(1)°. The observed density is 1.60 g/cm³ and the density calculated for four molecules in the cell is 1.58 g/cm³. The refinement converged with R = 0.029 and R_w = 0.028 based on 2569 reflections with I > 2.5 σ. The molecule has approximate C_s symmetry with a mirror plane roughly containing the central Mo atom and two cis-carbonyls, C(1)O(1) and C(4)O(4), while bisecting the bidentate, H₂CPz₂, and two trans-carbonyls. The four carbonyls and tine bidentate adopt a quasi-octahedral arrangement around the Mo atom. The C(NN)₂Mo linkage of the (H₂CPz′₂)Mo fragment is observed to be in the boat form. The two cis-carbonyls are bent away by the bulky H₂CPz′₂ bidentate giving ∠C(1)-Mo-C(4) ? 167.3(1)°. The distortion explains the facile allyl bromination and decarbonylation observed for the title compound.     

Organotransition-Metal Complexes of Multidentate Ligands 6. Electronic and Steric Influences on the Formation of η2-Acyl Complexes

Three new η²-acyl complexes, TMo(CO)₂(η²-COR) (T = Tp', Tp'; R= Me, Buⁿ; Tp' = hydridotris(3,5-dimethyl-pyrazol-1-yl)borate; Tp' = hydridotris(3,4,5-trimethylpyrazol-l-yl)borate) prepared from the corresponding alkyl iodides, RI, and the anions, TMo(CO)^?₃. The preparation of Et₄N⁺Tp Mo(CO)₃^? is also described. Using solution IR spectra to monitor the reactions between RI and TMo(CO)₃^?, it was found that Tp'Mo(CO)₂(η²-COMe) was formed more readily than Tp'Mo(CO)₂(η²-COMe) which was obtained more easily than Tp'Mo(CO)₂(η²-COBuⁿ). This finding suggests that the mechanism is probably an ionic substitution rather than a radical mechanism. The different times required for the complete conversion from the anions to TMo(CO)₂(η²-COR) is rationalized in terms of the electronic and steric influences of T and RI.     

Synthesis and application of diphenylbis (3,5-dimethylpyrazol-1-yl)methane to form η-arene complexes of molybdenum

The neutral nitrogen-bidentate ligand, diphenylbis(3,5-dimethylpyrazol-1-yl)methane, Ph₂CPz′₂, can readily be obtained by the reaction of Ph₂CCl₂ with excess HPz′ in a mixed-solvent system of toluene and triethylamine. It reacts with [Mo(CO)₆] in 1,2-dimethoxyethane to give the η²-arene complex, [Mo(Ph₂CPz′₂)(CO)₃] (1). This η²-ligation appears to stabilize the coordination of Ph₂CPz′ ₂ in forming [Mo(Ph₂CPz′₂)(CO)₂(N₂C₆H₄NO₂-p)][BPh₄] (2) and [Mo(Ph₂CPz′₂)(CO)₂(N₂Ph)] [BF₄] (3) from the reaction of 1 with the appropriate diazonium salt but the stabilization seems not strong enough when [Mo{P(OMe)₃} ₃(CO)₃] is formed from the reaction of 1 with P(OMe)₃. The solid-state structures of 1 and 3 have been determined by X-ray crystallography: 1-CH₂Cl₂, monoclinic, P2₁/n, a = 11.814(3), b = 11.7929(12), c = 19.46 0(6) Å, β = 95.605(24)°, V = 2698.2(11) ų, Z = 4, D_calc = 1.530 g/cm³ , R = 0.044, R_w = 0.036 based on 3218 reflections with I > 2σ(I); 2 (3)-1/2 hexane-1/2 CH₃OH-1/2 H₂O-1 CH₂Cl₂, monoclinic, C2/c, a = 41.766(10), b = 20.518(4), c = 16.784(3) Å, β = 101.871(18)°, V = 14076(5) ų, Z = 8, D_calc = 1.457 g/cm³, R = 0.064, R_w = 0.059 based on 5865 reflections with I > 2σ(I). Two independent cations were found in the asymmetric unit of the crystals of 3. The average distance between the Mo and the two η²-ligated carbon atoms is 2.574 Å in 1 and 2.581 and 2.608 Å in 3. The unfavourable disposition of the η²-phenyl group with respect to the metal centre in 3 and the rigidity of the η²-arene ligation excludes the possibility of any appreciable agostic C---H → Mo interaction.     

Tandem mass spectrometric strategies for determination of sulfation positions and uronic acid epimerization in chondroitin sulfate oligosaccharides

Chondroitin sulfate (CS) is a glycosaminoglycan consisting of repeating (HexA-GalNAc sulfate) disaccharides, the functions of which depend on patterns of sulfation and uronic acid epimerization. The correlation of biological activities with structure requires a strategy to determine the sequences of CS oligosaccharides without the need for total isolation. Tandem mass spectrometry has enabled the development of proteomics, based on CID fragmentation of ions produced from complex mixtures of proteolytic peptides, and has the potential for rapid sequencing of CS and other glycosaminoglycan classes. The most challenging aspects of CS sequencing are to distinguish GalNAc residues sulfated at the 4- versus the 6-position and uronic acid epimers. This work describes the utility of (1) reducing terminal derivatives and (2) control of precursor ion charge state for tandem mass spectrometric strategies for determining GalNAc sulfation positional isomers of CS. The capability of tandem MS to differentiate uronic acid epimers is also shown, providing evidence that complete or nearly complete information on CS covalent structure may be obtained using tandem MS.     

Six new 2-(2-phenylethyl)chromones from Agarwood

Six new chromones, 6-methoxy-2-[2-(3-methoxy-4-hydroxyphenyl)ethyllchromone (2), 6,8-dihydroxy-2-(2-phenylethyl)chromone (3), 6-hydroxy-2-[2-(4-hydroxyphenyl)ethyl]chromone (4), 6-hydroxy-2-[2-(2-hydroxyphenyl)ethyl]chromone (5), 7-hydroxy-2-(2-phenylethyl)chromone (6), and 6-hydroxy-7-methoxy-2-(2-phenylethyl)chromone (7) were isolated from the ether extract of agarwood in addition to a known compound, 2-(2-phenylethyl)chromone or flidersiachromone (1). Their structures were determined by spectroscopic methods including UV, IR, and NMR spectral data and comparisons with the calculated values using the hydroxyl and methoxyl substituent increments of the chromone ring.     

A complete characterization for <Emphasis Type="Italic">k</Emphasis>-resonant Klein-bottle polyhexes

A hexagonal tessellation K(p, q, t) on Klein bottle, a non-orientable surface with cross-cap number 2, is a finite-sized elemental benzenoid which can be produced from a p × q-parallelogram of hexagonal lattice with usual identifications of sides and with torsion t. Unlike torus, Klein bottle polyhex K(p, q, t) is not transitive except for some degenerated cases. We shall show, however, that K(p, q, t) does not depend on t. Accordingly, criteria for K(p, q, t) to be k-resonant for every positive integer k will be given. Moreover, we shall show that K(3, q, t) of 3-resonance are fully-benzenoid.