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.

Studies on some generalizations of line graph and the power domination problem in graphs

Department of Mathematics, Cochin University of Science and Technology

Studies on the Vertical Structure of Horizontal Wind Variability in the Surface Boundary Layer Over Sriharikota

The present study on the vertical structure of horizontal wind variability in the surface boundary layer over Sriharikota. Based on clock wind speed and direction measuring meteorological tower facility from seven levels in the 100 m layer. The study on wind variability and elliptical approximation of wind hodographs investigated for this tropical coastal station established that Sriharikota is of meso-scale weather entity. Wind variability ratio increases from lower levels to upper levels. In South West monsoon months the station is of high ratio values and it gets affected with meso-scale weather features like thunderstorms. Average total shears are observed greater values than scalar shears. Scalar shears are high in the lowest shear levels compared to upper levels. Semi diurnal types of oscillation in average total shears are found in south west monsoon months. During cyclonic storm passage it is observed that there can be significant difference in mean wind speed from 10 m to 100 m level, but it is not so for peak wind speeds. The variations in wind variability ratio in different months is clearly depicted its strong link to define meso-scale or synoptic –scale forcing domination for this station. Meso-scale forcing is characterized by diurnal wind variability and synoptic- scale forcing by interdiurnal wind variability.

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.

Studies on Some Graph Classes

Department of Mathematics, Cochin University of Science and Technology

‘Studies on some topics in product graphs’

For routing problems in interconnection networks it is important to find the shortest containers between any two vertices, since the w-wide diameter gives the maximum communication delay when there are up to w−1 faulty nodes in a network modeled by a graph. The concept of ‘wide diameter’ was introduced by Hsu [41] to unify the concepts of diameter and The concept of ‘domination’ has attracted interest due to its wide applications in many real world situations [38]. A connected dominating set serves as a virtual backbone of a network and it is a set of vertices that helps in routing. In this thesis, we make an earnest attempt to study some of these notions in graph products. This include, the diameter variability, the diameter vulnerability, the component factors and the domination criticality.connectivity

A study on mitigating the effect of sulphates in lime stabilised Cochin marine clays

Soft clays known for their high compressibility, low stiffness and low shear strength are always associated with large settlement. In place soil treatment using calcium-based stabilizers like lime and cement is a feasible solution to readdress strength deficiencies and problematic shrink/swell behaviour of unstable subgrade soils. Out of these, lime has been proved unambiguously as the most effective and economical stabilising agent for marine clays. Lime stabilisation creates long-term chemical changes in unstable clay soils to create strong, but flexible, permanent structural layers in foundations and other pavement systems. Even though calcium-based stabilizers can improve engineering properties of soft clays, problems can arise when they are used in soils rich in sulphates. It is possible for marine clays to be enriched with sulphates, either by nature or due to the discharge of nearby industrial wastes containing sulphates. The presence of sulphates is reported to adversely affect the cation exchange and pozzolanic reactions of cement and lime treated soil systems. The anions of sulphates may combine with the available calcium and alumina, and form insoluble ettringite in the soil system. Literature on sulphate attack in lime treated marine clays reports that formation of ettringite in lime-sodium sulphate-clay system is capable of adversely affecting the engineering behavior of marine clays. Only very few studies have been conducted on soft marine clays found along the coastal belt of Kerala and that too, is limited to Cochin marine clays. The studies conducted also have the limitation that the strength behaviour of lime stabilised clay was investigated only for one year. Practically no data pertaining to long term adverse effects likely to be brought about by sulphates on the strength and compressibility characteristics of Cochin marine clays is available. The overriding goal of this investigation was thus to examine the effectiveness of lime stabilisation in Cochin marine clays under varying sulphate contents. The study aims to reveal the changes brought about by varying sulphate contents on both physical and engineering properties of these clays stabilised by lime and the results for various curing periods up to two years is presented in this thesis. Quite often the load causing an unacceptable settlement may be less than the load required to cause shear failure and therefore attempt has been made in this research to highlight sulphate induced changes in both the compressibility and strength characteristics of lime treated Cochin marine clays. The study also aimed at comparing the available IS methods for sulphate quantification and has attempted to determine the threshold level of sulphate likely make these clays vulnerable by lime stabilisation. Clays used in this study were obtained from two different sites in Kochi and contained sulphate in two different concentrations viz., 0.5% and 0.1%. Two different lime percentages were tried out, 3% and 6%. Sulphate content was varied from 1% to 4% by addition of reagent grade sodium sulphate. The long term influence of naturally present sulphate is also investigated. X-ray diffraction studies and SEM studies have been undertaken to understand how the soil-lime reactions are affected in the presence of sodium sulphate. Natural sulphate content of 0.1% did not seem to have influenced normal soil lime reactions but 0.5% sulphate could induce significant changes adversely in both compressibility and strength behaviour of lime treated clays after long duration. Compressibility is seen to increase drastically with increasing sulphate content suggesting formation of ettringite on curing for longer periods. Increase in compression index and decrease in bond strength with curing period underlined the adverse effects induced in lime treated marine clays by the presence of sulphates. Presence of sulphate in concentrations ranging from 0.5 % to 4% is capable of adversely affecting the strength of lime treated marine clays. Considerable decrease is observed with increasing concentrations of sulphate. Ettringite formation due to domination of sodium ions in the system was confirmed in mineralogical studies made. Barium chloride and barium hydroxide is capable of bringing about beneficial changes both in compressibility and strength characteristics of lime treated Cochin marine clays in the presence of varying concentrations of sulphate and is strongly influenced by curing time. Clay containing sodium sulphate has increased strength values when either of barium compounds was used with lime ascompared with specimens treated with lime only. Barium hydroxide is observed to remarkably increase the strength as compared to barium chloride,when used in conjunction with lime to counteract the effect of sulphate.