The P3 Intersection Graph

We define a new graph operator called the P3 intersection graph, P3(G)- the intersection graph of all induced 3-paths in G. A characterization of graphs G for which P-3 (G) is bipartite is given . Forbidden subgraph characterization for P3 (G) having properties of being chordal , H-free, complete are also obtained . For integers a and b with a > 1 and b > a - 1, it is shown that there exists a graph G such that X(G) = a, X(P3( G)) = b, where X is the chromatic number of G. For the domination number -y(G), we construct graphs G such that -y(G) = a and -y (P3(G)) = b for any two positive numbers a > 1 and b. Similar construction for the independence number and radius, diameter relations are also discussed.

The Edge C4 Graph of a Graph

Abstract. The edge C4 graph E4(G) of a graph G has all the edges of Gas its vertices, two vertices in E4(G) are adjacent if their corresponding edges in G are either incident or are opposite edges of some C4. In this paper, characterizations for E4(G) being connected, complete, bipartite, tree etc are given. We have also proved that E4(G) has no forbidden subgraph characterization. Some dynamical behaviour such as convergence, mortality and touching number are also studied

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.

Surface electron properties and catalytic activity of cerium-zirconium mixed oxides

The electron donating properties, surface acidity/ basicity and catalytic activity of cerium - zirconium mixed oxides at various compositions have been reported at an activation temperature of 500 degree C. The catalytic activity for the esterification of acetic acid with n-butanol has heen correlated with electron donating properties and surface acidity/basicity of the oxides.

Alkylation of phenol with methanol over mixed oxides of tin with some rare earth elements

Alkylation of phenol with methanol has been carried out over Sn-La and Sn-Sm mixed oxides of varying compositions at 623 K in a vapour phase flow reactor. It is found that the product selectivity is greatly influenced by the acid-base properties of the catalysts. Ortho-cresol formation is favoured over catalysts with weak acid sites whereas formation of 2,6-xylenol occurs in the presence of stronger acid sites. The cyclohexanol decomposition reaction and titrimetric method using Hammett indicators have been employed to elucidate the acid-base properties of the catalysts.

Surface acidity and catalytic activity of mixed Fe-Al and Cr-Al pillared montmorillonites

The incorporation of transition metal oxide pillars such as those of iron and chromium along with Al2O3, pillars within the interlayers of a montmorillonite clay is investigated. The surface acidity of these catalysts has been evaluated for the first time employing the equilibrium adsorption of an electron donor, perylene, and the results are compared with those obtained by temperature programmed desorption of ammonia. The principle is based on the ability of a catalyst surface site to accept a single electron from an electron donor like perylene to form charge transfer complexes and the amount of adsorbed species is measured quantitatively by UV-vis spectroscopy. Fina1ly, an attempt has been made to correlate the acidity determined by the two independcnt methods and the catalytic activity of present systems in the benzoylation of toluene with benzoyl chloride. Incorporation of Fe and Cr has changed the properties of AI pitlared montmorillonite. Fe pillared systems have been found to be vcry good catalysts for benzoylation reaction

Electron donating properties and catalytic actiVity of cerium oxide and its mixed oxides with alumina

The electron donating properties of Ce02 and its mixed oxides with alumina have been determined from the studies of adsorption of electron acceptors of various electron affinities on the surface of these oxides. The catalytic activity of these oxides towards some reactions such as oxidation of alcohols and reduction of ketones have been Correlated with their surface electrondonor properties. The surface acidity/basicity of these oxides have also been determined by titration method using a set of Hammett indicators.

Basicity and electron donor properties of lanthanum oxide and its mixed oxides with alumina

The electron donating properties of La2O3 activated at 300, 500 and 800·C and its mixed oxides with alumina are reported from the studies on adsorption of electron acceptors of varying electron affinity on La203. The electron acceptors with their electron affinity values given in parenthesis are: 7,7,8,8-tetracyanoquinodimethane (2.84 eV), 2,3,5,6-tetrachloro-I,4-benzoquinone (2.40 eV) and p-dinitrobenzene(l.77eV). The basicity of the oxide has been determined by titration with n-butylamine and Ho.max values are reported. The limit of electron transfer from the oxide to the electron acceptor is between 2.40 and 1.77 eV. It is observed that La203 promotes the surface electron properties of alumina without changing its limit of electron transfer.

Surface acidity/basicity and catalytic activity of Zr-Sm mixed oxide systems

The surface acidity and basicity of oxides of Sm and Zr and their mixed oxides have been determined using a set of Hammett indicators. The data have been correlated with the catalytic activity of these oxides towards the liquid phase reduction of cyclo-hexanone in 2-propanol.