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

Studies on some graph operators and related topics

Department of Mathematics, Cochin University of Science and Technology

Investigations on Structural response of Water Backed Perforated plates

The study envisaged herein contains the numerical investigations on Perforated Plate (PP) as well as numerical and experimental investigations on Perforated Plate with Lining (PPL) which has a variety of applications in underwater engineering especially related to defence applications. Finite element method has been adopted as the tool for analysis of PP and PPL. The commercial software ANSYS has been used for static and free vibration response evaluation, whereas ANSYS LS-DYNA has been used for shock analysis. SHELL63, SHELL93, SOLID45, SOLSH190, BEAM188 and FLUID30 finite elements available in the ANSYS library as well as SHELL193 and SOLID194 available in the ANSYS LS-DYNA library have been made use of. Unit cell of the PP and PPL which is a miniature of the original plate with 16 perforations have been used. Based upon the convergence characteristics, the utility of SHELL63 element for the analysis of PP and PPL, and the required mesh density are brought out. The effect of perforation, geometry and orientation of perforation, boundary conditions and lining plate are investigated for various configurations. Stress concentration and deflection factor are also studied. Based on these investigations, stadium geometry perforation with horizontal orientation is recommended for further analysis.Linear and nonlinear static analysis of PP and PPL subjected to unit normal pressure has been carried out besides the free vibration analysis. Shock analysis has also been carried out on these structural components. The analytical model measures 0.9m x 0.9m with stiffener of 0.3m interval. The influence of finite element, boundary conditions, and lining plate on linear static response has been estimated and presented. Comparison of behavior of PP and PPL in the nonlinear strain regime has been made using geometric nonlinear analysis. Free vibration analysis of the PP and PPL has been carried out ‘in vacuum’ condition and in water backed condition, and the influence of water backed condition and effect of perforation on natural frequency have been investigated.Based upon the studies on the vibration characteristics of NPP, PP and PPL in water backed condition and ‘in vacuum’ condition, the reduction in the natural frequency of the plate in immersed condition has been rightly brought out. The necessity to introduce the effect of water medium in the analysis of water backed underwater structure has been highlighted.Shock analysis of PP and PPL for three explosives viz., PEK, TNT and C4 has been carried out and deflection and stresses on plate as well as free field pressure have been estimated using ANSYS LS-DYNA. The effect of perforations and the effect of lining plate have been predicted. Experimental investigations of the measurement of free field pressure using PPL have been conducted in a shock tank. Free field pressure has been measured and has been validated with finite element analysis results. Besides, an experiment has been carried out on PPL, for the comparison of the static deflection predicted by finite element analysis.The distribution of the free field pressure and the estimation of differential pressure from experimentation and the provision for treating the differential pressure as the resistance, as a part of the design load for PPL, has been brought out.

The influence of organophosphorus pesticide-methylparathion on protein, lipid metabolism and detoxifying enzymes in rohu (Labeo rohita)

Methylparathion (MP) is an organophosphorus insecticide used world wide in agriculture due to its high activity against a broad spectrum of insect pests. The aim of the study is to understand the effect of methylparathion on the lipid peroxidation, detoxifying and antioxidant enzymes namely catalase (CAT), glutathione peroxidase (GPx), superoxide dismutase (SOD), glutathione Stransferase (GST), total reduced glutathione (GSH), lipid peroxidation (LPO), acetylcholinesterase (AChE) and disease diagnostic marker enzymes in liver, sarcoplasmic (SP) and myofirbirllar (MF) proteins in muscles, lipids and histopathlogical changes in various organs of Labeo rohita of size 75 i 6g at lethal and sublethal level of exposure. The probit analysis showed that the lethal concentration (LC 50%) for 24, 48, 72 and 96h were 15.5mg/L, 12.3mg/L, 11.4mg/L and 10.2mg/L respectively which is much higher compared to the LC50 for juvenile fish. The LPO level and GST activity increased five folds and two folds respectively on exposure to methylparathion at 10.2 mg/L and the level of the enzymes increased, on sub lethal exposure beyond 0.25mg/L. AChE activity was inhibited by 74% at a concentration of 1.8mg/L and 90% at 5.4mg/L. The disease diagnostic marker enzymes AST, ALT, ALP and LDH increased by about 2, 3 ,3 and 2 folds respectively at pesticide concentration of 10.2mg/L when compared to control. On sub lethal exposure, however the enzymes did not show any significant changes up to 0.5mg/L. At a concentration of 10.2 mg/L, there was a three fold increase in myofibrillar proteins while the increase in sarcoplasmic protein was above 1.5 fold. On sub lethal exposure, significant alteration was noticed up to 30 days up to 1mg/L of methylparathion concentration. Further exposure up to 45 days increased sarcoplasmic proteins (upto 0.5mg/L). ln the case of myofibrillar proteins, noticeable changes were observed at 1mg/L concentration right from 15th day. The cholesterol content in brain tissues increased by about 27% at methylparathion concentration of 5.4 mglL. However at 0.25mg/L sub lethal concentration, no significant alteration was observed in enzyme activity, muscle proteins, lipids and histopathology of the tissues. The results suggest that methylparathion has the potential to induce oxidative stress in fish, and that liver, muscle and brains are more sensitive organs of Labeo rohita, with poor antioxidant potentials at higher concentrations of the pesticide. The various parameters studied in this investigation can also be used as biomarkers of methylparathion exposure.

A Novel Decision Tree Algorithm for Numeric Datasets - C 4.5*Stat

Decision trees are very powerful tools for classification in data mining tasks that involves different types of attributes. When coming to handling numeric data sets, usually they are converted first to categorical types and then classified using information gain concepts. Information gain is a very popular and useful concept which tells you, whether any benefit occurs after splitting with a given attribute as far as information content is concerned. But this process is computationally intensive for large data sets. Also popular decision tree algorithms like ID3 cannot handle numeric data sets. This paper proposes statistical variance as an alternative to information gain as well as statistical mean to split attributes in completely numerical data sets. The new algorithm has been proved to be competent with respect to its information gain counterpart C4.5 and competent with many existing decision tree algorithms against the standard UCI benchmarking datasets using the ANOVA test in statistics. The specific advantages of this proposed new algorithm are that it avoids the computational overhead of information gain computation for large data sets with many attributes, as well as it avoids the conversion to categorical data from huge numeric data sets which also is a time consuming task. So as a summary, huge numeric datasets can be directly submitted to this algorithm without any attribute mappings or information gain computations. It also blends the two closely related fields statistics and data mining