ON DISTANCE ENERGY OF GRAPHS

The D-eigenvalues of a graph G are the eigenvalues of its distance matrix D, and the D-energy ED(G) is the sum of the absolute values of its D-eigenvalues. Two graphs are said to be D-equienergetic if they have the same D-energy. In this note we obtain bounds for the distance spectral radius and D-energy of graphs of diameter 2. Pairs of equiregular D-equienergetic graphs of diameter 2, on p = 3t + 1 vertices are also constructed.

GALLAI AND ANTI-GALLAI GRAPHS OF A GRAPH

Abstract. The paper deals with graph operators-the Gallai graphs and the anti-Gallai graphs. We prove the existence of a finite family of forbidden subgraphs for the Gallai graphs and the anti-Gallai graphs to be H-free for any finite graph H. The case of complement reducible graphs-cographs is discussed in detail. Some relations between the chromatic number, the radius and the diameter of a graph and its Gallai and anti-Gallai graphs are also obtained.

Studies on Some Transition Metal Complexes of Schiff Bases Derived from Quinoxaline-2-carboxaldehyde

Two series of transition metal complexes of Schiff bases derived from quinoxaline-2-carboxaldehyde with semicarbazide (QSC) and furfurylamine (QFA) were synthesised and characterised by elemental analyses, molar conductance and magnetic susceptibility measurements, IR, electronic and EPR spectral studies. The QSC complexes have the general formula [M(QSC)Cl2]. A tetrahedral structure has been assigned for the Mn(II), Co(II) and Ni(II) complexes and a square-planar structure for the Cu(II) complex. The QFA complexes have the formula [M(QFA)2Cl2]. An octahedral structure has been assigned for these complexes. All of the complexes exhibit catalytic activity towards the oxidation of 3,5-di-tert-butylcatechol (DTBC) to 3,5-di-tert-butylquinone (DTBQ) using atmospheric oxygen. The cobalt(II) complex of the ligand QFA was found to be the most active catalyst.

Synthesis and Characterization of Some New Transition Metal Complexes of the Schiff Base Derived from Quinoxaline-2-Carboxaldehyde and 2- Aminophenol

Some new transition metal complexes of the Schiff base quinoxaline-2-car boxalidene-2-aminophenol (HQAP) have been synthesized and characterized by elemental analyses, conductance and magnetic measurements and IR and UV-Visible spectral studies. The complexes have the following empirical formulae: [Mn(QAP121, [Fe(QAPl2C1I, [Co(QAPl21, [Ni(QAP121 and [Cu(QAP121. A tetrahedral structure has been assigned for the manganese(=), cobalt(II1, nickel(II1 and copper(II1 complexes. For the iron(IIIl complex an octahedral dimeric structure has been suggested

Synthesis and Characterisation of New Transition Metal Complexes of Schiff Bases Derived from 3-hydroxyquinoxaline-2- carboxaldehyde and Application of Some ofthese Complexes as Hydrogenation and Oxidation Catalysts

The thesis deals with studies on the synthesis, characterisation and catalytic applications of some new transition metal complexes of the Schiff bases derived from 3-hydroxyquinoxaline 2-carboxaldehyde.. Schiff bases which are considered as ‘privileged ligands’ have the ability to stabilize different metals in different oxidation states and thus regulate the performance of metals in a large variety of catalytic transformations. The catalytic activity of the Schiff base complexes is highly dependant on the environment about the metal center and their conformational flexibility. Therefore it is to be expected that the introduction of bulky substituents near the coordination sites might lead to low symmetry complexes with enhanced catalytic properties. With this view new transition metal complexes of Schiff bases derived from 3-hydroxyquinoxaline-2-carboxaldehyde have been synthesised. These Schiff bases have more basic donor nitrogen atoms and the presence of the quinoxaline ring may be presumed to build a favourable topography and electronic environment in the immediate coordination sphere of the metal. The aldehyde was condensed with amines 1,8-diaminonaphthalene, 2,3-diaminomaleonitrile, 1,2-diaminocyclohexane, 2-aminophenol and 4-aminoantipyrine to give the respective Schiff bases. The oxovanadium(IV), copper(II) and ruthenium(II)complexes of these Schiff bases were synthesised and characterised. All the oxovanadium(IV) complexes have binuclear structure with a square pyramidal geometry. Ruthenium and copper form mononuclear complexes with the Schiff base derived from 4- aminoantipyrine while binuclear square planar complexes are formed with the other Schiff bases. The catalytic activity of the copper complexes was evaluated in the hydroxylation of phenol with hydrogen peroxide as oxidant. Catechol and hydroquinone are the major products. Catalytic properties of the oxovanadium(IV) complexes were evaluated in the oxidation of cyclohexene with hydrogen peroxide as the oxidant. Here allylic oxidation products rather than epoxides are formed as the major products. The ruthenium(II) complexes are found to be effective catalysts for the hydrogenation of benzene and toluene. The kinetics of hydrogenation was studied and a suitable mechanism has been proposed.

Organometallic Hydroxides of Transition Elements

Northern Illinois University DeKalb,Institut fu¨r Anorganische Chemie & Southern Methodist University

Antimedian graphs

Antimedian graphs are introduced as the graphs in which for every triple of vertices there exists a unique vertex x that maximizes the sum of the distances from x to the vertices of the triple. The Cartesian product of graphs is antimedian if and only if its factors are antimedian. It is proved that multiplying a non-antimedian vertex in an antimedian graph yields a larger antimedian graph. Thin even belts are introduced and proved to be antimedian. A characterization of antimedian trees is given that leads to a linear recognition algorithm.

Thermal Properties of Dicalcium Lead Propionate Across the Prominent Transition Temperatures

The thermal transport properties, thermal diffusivity, thermal conductivity and specific heat capacity of Dicalcium Lead Propionate (DLP) crystal have been measured following a modified photopyroelectric thermal wave method. The measurements have been carried out with thermal waves propagating along the three principal symmetry directions, so as to bring out the anisotropy in these parameters. The variations of the above parameters through two prominent phase transition temperatures of this crystal have also been measured to understand the variation of these parameters as it undergoes ferroelectric phase transitions. In addition, complete thermal analysis and FTIR measurements have been done on the crystal to bring out the correlation of these results with the corresponding thermal transport properties. All these results are presented and discussed. The data presented in this paper form a comprehensive set of results on the thermal transport properties of this crystal.

Energies of some non-regular graphs

The energy of a graph G is the sum of the absolute values of its eigenvalues. In this paper, we study the energies of some classes of non-regular graphs. Also the spectrum of some non-regular graphs and their complements are discussed.