A Note On Some Domination Parameters in Graph Products

In this paper, we study the domination number, the global dom ination number, the cographic domination number, the global co graphic domination number and the independent domination number of all the graph products which are non-complete extended p-sums (NEPS) of two graphs.

Mixed layer characteristics and hydrography off the west and east coasts of India

In this thesis, a detailed attempt has been made to understand the general hydrography of the upper 300m of the water column, in the eastern Arabian Sea and the western Bay of Bengal, the two contrasting basins in the northern Indian Ocean, using recently collected data sets of Marine Research-Living Resources (MR-LR) assessment programme, funded by Department of Ocean Development, from various cruises, pertaining to different seasons. Initially it discuss the general hydrography of the west and east coasts of India are covered, in the context of mixed layer processes. The study describes the materials and methods . To compare the hydrography of the AS and BOB, a unique MLD(Mixed Layer Depth) definition for AS and BOB is essential, for which the 275 CTD profiles were used. A comparison has been made among the various MLD criteria with the actual MLD. The monthly evolution of MLD, barrier layer thickness and the role of atmospheric forcing on the dynamics of the mixed layer in the AS and BOB were studied. The general hydrography along the west coast of India is described. The upwelling/downwelling, winter cooling processes, in the context of chemical and biological parameters, are also addressed. Finally the general hydrography of the Bay of Bengal is covered. The most striking feature in the hydrography are the signature of an anticyclonic subtropical gyre during spring intermonsoon and a cold core eddy during winter monsoon. The TTS(Typical Tropical Structure) of the euphotic layer was also investigated.

Ultrasonic Study Of The Elastic Properties And Phase Transitions In Selected Mixed Sulphate Crystals

The thesis investigated the elastic properties and phase transitions in selected mixed sulphate crystals – Lithium Hydrazinium Sulphate [LiN2H2SO4], Lithium Ammonium Sulphate [LiNH4SO4] and Lithium Potassium Sulphate [LiKSO4] – using ultrasonic technique. The pulse echo overlap technique has been used for measuring ultrasonic velocity and its dependence on temperature along different directions with waves of longitudinal and transverse polarizations. Two major numerical techniques and the corresponding computer programs developed as part of present work are presented in this thesis. All the 9 elastic constants of LHS are determined accurately from ultrasonic measurements and applying misorientation correction refines the constants. Ultrasonic measurements are performed in LAS to determine the elastic constants and to study the low temperature phase transitions. Temperature variation studies of elastic constant of LAS are performed for 6 different modes of propagation for heating and cooling at low temperatures. All the 5 independent elastic constants of LPS is determined using ultrasonic measurements. It is concluded that LPS crystal does not undergo a phase transition near this temperature. A comparison of the three crystals studied shows that LPS has maximum number of phase transitions and LHS has the least number. It is interesting to note that LPS has the simplest formula unit among the three. There is considerable scope for the future work on these crystals and others belonging to the sulphate family.

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.