The Connected Monophonic Number of a Graph

For a connected graph G = (V, E) of order at least two, a chord of a path P is an edge joining two non-adjacent vertices of P. A path P is called a monophonic path if it is a chordless path. A set S of vertices of G is a monophonic set of G if each vertex v of G lies on an x ? y monophonic path for some elements x and y in S. The minimum cardinality of a monophonic set of G is defined as the monophonic number of G, denoted by m(G). A connected monophonic set of G is a monophonic set S such that the subgraph G[S] induced by S is connected. The minimum cardinality of a connected monophonic set of G is the connected monophonic number of G and is denoted by m _c (G). We determine bounds for it and characterize graphs which realize these bounds. For any two vertices u and v in G, the monophonic distance d _m (u, v) from u to v is defined as the length of a longest u ? v monophonic path in G. The monophonic eccentricity e _m (v) of a vertex v in G is the maximum monophonic distance from v to a vertex of G. The monophonic radius rad _m G of G is the minimum monophonic eccentricity among the vertices of G, while the monophonic diameter diam _m G of G is the maximum monophonic eccentricity among the vertices of G. It is shown that for positive integers r, d and n ≥ 5 with r <  d, there exists a connected graph G with rad _m G =  r, diam _m G =  d and m _c (G) =  n. Also, if a,b and p are positive integers such that 2 ≤  a <  b ≤  p, then there exists a connected graph G of order p, m(G) =  a and m _c (G) =  b.     

A sensitive amperometric detection of dopamine agonist drug pramipexole at functionalized multi-walled carbon nanotubes (f-MWCNTs) modified electrode

The electrochemical detection of dopaminergic agonist drug pramipexole dihydrochloride monohydrate (PPX) has been investigated by cyclic voltammetric (CV) and amperometric i–t techniques at functionalized multi-walled carbon nanotubes-modified glassy carbon electrode. For the first time, a sensitive and rapid electrochemical method was developed for the determination of PPX. The surface morphological characteristics of the proposed electrode have been studied by using transmission electron microscopy (TEM); further, electrochemical impedance spectroscopy (EIS) and Fourier transform infrared spectroscopy (FTIR) have been employed. PPX shows an irreversible anodic peak, which may be ascribed to the oxidation of the –NH groups of PPX. The proposed method was showing good sensitivity of 0.993 μA μM^?1 cm^?2 with a linear range of 5 to 340 μM by amperometric i–t and CV technique shows a linear range of 12.5 to 313 μM with a sensitivity of 1.92 μA μM^?1 cm^?2. The recovery of PPX from blood serum samples was found 100.6 and 98.9 %, respectively. Furthermore, the proposed method has been demonstrated for the determination of PPX in commercially available pharmaceutical samples and good agreement of results obtained.     

Synthesis and Structural Characterization of Magnesium‐Substituted Polystibides [(LMg)4Sb8]

Redox reactions of [(L^1,2Mg)₂] and Sb₂R₄ (R=Me, Et) yielded the first Mg‐substituted realgar‐type Sb₈ polystibides [(L^1,2Mg)₄(μ₄,η^2:2:2:2‐Sb₈)] (L¹=HC[C(Me)N(2,4,6‐Me₃C₆H₂)]₂, L²=HC[C(Me)N(2,6‐i‐Pr₂C₆H₃)]₂). Compounds [(L^1,2Mg)₂] serve both as reducing agents, initiating the cleavage of the Sb?C bonds, and as stabilizers for the resulting Sb₈ polyanion. The polystibides were characterized by NMR and IR spectroscopies, elemental analysis, and X‐ray structure analysis. In addition, results from quantum chemical calculations are presented.     

Growth of Inclusion Free KTP Crystals by Top Seeded Solution Growth and their Characterization

KTiOPO₄ single crystals of dimensions 34 × 15 × 15 mm³ have successfully been grown by Top Seeded Solution Growth (TSSG), using phosphate flux (K₆P₄O₁₃), employing a home made vertical cylindrical three zone resistive heated furnace. Growth experiments were carried out with <001> seed orientation. A method to grow inclusion free crystal with less dislocation density is proposed, by employing cooling rate of 0.5‐2 K/day and rotation rate of 60‐30 rpm. UV‐VIS transmission studies were performed and the dependence of absorption coefficient with wavelength is discussed. SHG elements of dimension 8 × 7.5 × 7.5 mm³ were fabricated and conversion efficiency of 58 % was achieved without antireflection coating. Nature of ionic conductivity and ferroelectric phase transition behavior of KTP crystals along the crystallographic polar axis in the frequency range of 100 Hz – 10 MHz are discussed.     

Investigations on the Nucleation Thermodynamics of RbTiOXO4 (X = P or As) Crystals Grown from High Temperature Solution

The nucleation thermodynamics of RbTiOXO₄ (where X = P or As) family crystals crystallizing from high temperature solution using the phosphate and tungstate solvents have been studied. Using the regular solution model and classical nucleation theory the nucleation thermodynamical parameters like interfacial energy, chemical potential, free energy change, critical energy barrier and radius of critical nucleus have been calculated which leads to better understanding of the nucleation process. Comparative study has also been made to investigate the metastable zone width of the above family crystals grown from different fluxes.     

Bi-, tetra-, and hexanuclear AuI and binuclear AgI complexes and AgI coordination polymers containing phenylaminobis(phosphonite), PhN{P(OC6H4OMe-o)2}2, and pyridyl ligands

The reactions of phenylaminobis(phosphonite), PhN{P(OC6H4OMe-o)2}2 (1) (PNP), with [AuCl(SMe2)] in appropriate ratios, afford the bi- and mononuclear complexes, [(AuCl)2(micro-PNP)] (2) and [(AuCl)(PNP)]2 (3) in good yield. Treatment of 2 with 2 equiv of AgX (X = OTf or ClO4) followed by the addition of 1 or 2,2'-bipyridine affords [Au2(micro-PNP)2](OTf)2 (4) and [Au2(C10H8N2)2(micro-PNP)](ClO4)2 (5), respectively. Similarly, the macrocycles [Au4(C4H4N2)2(micro-PNP)2](ClO4)4 (6), [Au4(C10H8N2)2(micro-PNP)2](ClO4)4 (7), and [Au6(C3H3N3)2(micro-PNP)3](ClO4)6 (8) are obtained by treating 2 with pyrazine, 4,4'-bipyridine, or 1,3,5-triazine in the presence of AgClO 4. The reaction of 1 with AgOTf in a 1:2 molar ratio produces [Ag2(micro-OTf)2(micro-PNP)] (9). The displacement of triflate ions in 9 by 1 leads to a disubstituted derivative, [Ag2(micro-PNP)3](OTf)2 (10). The equimolar reaction of 1 with AgClO4 in THF affords [Ag2(C4H8O)2(micro-PNP)2](ClO4)2 (11). Treatment of 1 with AgClO4 followed by the addition of 2,2'-bipyridine affords a discrete binuclear complex, [Ag2(C10H8N2)2(micro-PNP)](ClO4)2 (12), whereas similar reactions with 4,4'-bipyridine or pyrazine produce one-dimensional zigzag Ag (I) coordination polymers, [Ag2(C10H8N2)(micro-ClO4)(ClO4)(micro-PNP)]n (13) and [Ag2(C4H4N2)(micro-ClO4)(ClO4)(micro-PNP)]n (14) in good yield. The nature of metal-metal interactions in compounds 2, 4, 5, and 12 was analyzed theoretically by performing HF and CC calculations. The structures of the complexes 2, 4, 5, 7, 9, 12, and 14 are confirmed by single crystal X-ray diffraction studies.     

Occurrence of C-glucoside of resveratrol oligomers in Hopea parviflora

Investigation of the highly polar chemical constituents in the stem of Hopea parviflora (Dipterocarpaceae) resulted in the isolation of four new resveratrol derivatives, hopeasides A and B (1, 2) (resveratrol pentamers), C (3) (resveratrol trimer), and D (4) (resveratrol dimer) together with nine known resveratrol oligomers (5-13). The new structures have a common partial structure of the 1-hydroxy-1-(3,5-dihydroxy-2-C-glucopyranosylphenyl)-2-(4-hydroxyphenyl)ethane-2-yl group after oxidative condensation of (E)-resveratrol-10-C-β-glucopyranoside (14). The structures were determined by spectroscopic analysis including 2D-NMR and computer-aided molecular modeling. The biogenetic relationship of the isolates and NMR characteristics caused by steric hindrance are also discussed in this paper.     

ChemInform Abstract: Weak Interactions Between Trivalent Pnictogen Centers: Computational Analysis of Bonding in Dimers X3E···EX3 (E: Pnictogen,X: Halogen).

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