Axially Symmetric Radiation Patterns from Corrugated

A modified H-plane sectoral horn antenna with identical E- and'H- plane.patterns over the X-band frequency is discussed. This system has significantly reduced side lobes and hack lobes. Half=power beam width and gain of the antenna are also improved with enhanced matching , Experimental results for a number of horns with various flanges are presented . These find practical application for illuminating symmetric antennas like paraboloids and polarization measurements in radio astronomy, etc. Compared to the fixed pyramidal horns. the present system offers great convenience in trimming the antenna characteristics

The (t) property of some classes of graphs

In this note,the (t) properties of five class are studied. We proved that the classes of cographs and clique perfect graphs without isolated vertices satisfy the (2) property and the (3) property, but do not satisfy the (t) property for tis greater than equal to 4. The (t) properties of the planar graphs and the perfect graphss are also studied . we obtain a necessary and suffieient conditions for the trestled graph of index K to satisfy the (2) property

SOME NEW INTEGRAL GRAPHS

The eigenvalue of a graph is the eigenvalue of its adjacency matrix . A graph G is integral if all of its cigenvalues are integers. In this paper some new classes of integral graphs are constructed.

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.

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.

An approximation method for evaluating centrifugal distortion constants in XH2 bent symmetric molecules

University of Cochin

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

Department of Mathematics, Cochin University of Science and Technology

Bioactivity Profile of Polyunsaturated Fattyacid extracts from Sardinella longiceps and Sardinella fimbriata – A comparative study

The oceans have proved to be an interminable source of new and effective drugs. Innumerable studies have proved that specific compounds isolated from marine organisms have great nutritional and pharmaceutical value. Polyunsaturated fattyacids (PUFA) in general are known for their dietary benefits in preventing and curing several critical ailments including Coronary heart disease (CHD) and cancers of various kinds. Eicosapentaenoic Acid (EPA) and Docosahexaenoic Acid (DHA) are two PUFA which are entirely marine in origin – and small Clupeoid fishes like sardines are known to be excellent sources of these two compounds. In this study, we selected two widely available Sardine species in the west coast, Sardinella longiceps and Sardinella fimbriata, for a comparative analysis of their bioactive properties. Both these sardines are known to be rich in EPA and DHA, however considerable seasonal variation in its PUFA content was expected and these variations studied. An extraction procedure to isolate PUFA at high purity levels was identified and the extracts obtained thus were studied for anti-bacterial, anti-diabetic and anti-cancerous properties.Samples of both the sardines were collected from landing centre, measured and their gut content analysed in four different months of the year – viz. June, September, December and March. The fish samples were analyzed for fattyacid using FAME method using gas chromatography to identify the full range of fattyacids and their respective concentration in each of the samples. The fattyacids were expressed in mg/g meat and later converted to percentage values against total fatty acids and total PUFA content. Fattyacids during winter season (Dec-Mar) were found to be generally higher than spawning season (June-Sept). PUFA dominated the profiles of both species and average PUFA content was also higher during winter. However, it was found that S. longiceps had proportionately higher EPA as compared to S. fimbriata which was DHA rich. Percentage of EPA and DHA also varied across months for both species – the spawning season seemed to show higher EPA content in S. longiceps and higher DHA content in S. fimbriata. Gut content analysis indicate that adult S. fimbriata is partial to zooplanktons which are DHA rich while adult S. longiceps feed mainly on EPA rich phytoplankton. Juveniles of both species, found mainly in winter, had a gut content showing more mixed diet. This difference in the feeding pattern reflect clearly in their PUFA profile – adult S. longiceps, which dominate the catch during the spawn season, feeding mostly on phytoplankton is concentrated with EPA while the juveniles which are found mostly in the winter season has slightly less EPA proportion as compared to adults. The same is true for S. fimbriata adults that are caught mostly in the spawning season; being rich in DHA as they feed mainly on zooplankton while the juveniles caught during winter season has a relatively lower concentration of DHA in their total PUFA.Various extraction procedures are known to obtain PUFA from fish oil. However, most of them do not give high purity and do not use materials indicated as safe. PUFA extracts have to be edible and should not have harmful substances for applying on mice and human subjects. Some PUFA extraction procedures, though pure and non-toxic, might induce cis-trans conversions during the extraction process. This conversion destroys the benefits of PUFA and at times is harmful to human body. A method free from these limitations has been standardized for this study. Gas Chromatography was performed on the extracts thus made to ensure that it is substantially pure. EPA: DHA ratios for both samples were derived - for S. longiceps this ratio was 3:2, while it was 3:8 for S. fimbriata.Eight common strains of gram positive and gram negative bacterial strains were subjected to the PUFA extracts from both species dissolved in acetone solution using Agar Well Diffusion method. The activity was studied against an acetone control. At the end of incubation period, zones of inhibition were measured to estimate the activity. Minimum inhibitory concentration for each of the active combinations was calculated by keeping p < 0.01 as significant. Four of the bacteria including multi-resistant Staphylococcus aureus were shown to be inhibited by the fish extracts. It was also found that the extracts from S. fimbriata were better than the one from S. longiceps in annihilating harmful bacteria.Four groups of mice subjects were studied to evaluate the antidiabetic properties of the PUFA extracts. Three groups were induced diabetes by administration of alloxan tetra hydrate. One group without diabetes was kept as control and another with diabetes was kept as diabetic control. For two diabetic groups, a prescribed amount of fish extracts were fed from each of the extracts. The biochemical parameters like serum glucose, total cholesterol, LDL & HDL cholesterol, triglycerides, urea and creatinine were sampled from all four groups at regular intervals of 7 days for a period of 28 days. It was found that groups fed with fish extracts had marked improvement in the levels of total LDL & HDL cholesterol, triglycerides and creatinine. Groups fed with extracts from S. fimbriata seem to have fared better as compared to S. longiceps. However, both groups did not show any marked improvement in blood glucose levels or levels of urea.Cell lines of MCF-7 (Breast Cancer) and DU-145 (Prostate Cancer) were used to analyse the cytotoxicity of the PUFA extracts. Both cell lines were subjected to MTT Assay and later the plates were read using an ELISA reader at a wavelength of 570nm. It was found that both extracts had significant cytotoxic effects against both cell lines and a peak cytotoxicity of 85-90% was apparent. IC50 values were calculated from the graphs and it was found that S. longiceps extracts had a slightly lower IC50 value indicating that it is toxic even at a lower concentration as compared to extracts from S. fimbriata.This study summarizes the bioactivity profile of PUFA extracts and provides recommendation for dietary intake; fish based nutritional industry and indigenous pharmaceutical industry. Possible future directions of this study are also elaborated.

Clique Irreducibility and Clique Vertex Irreducibility of Graphs

A graphs G is clique irreducible if every clique in G of size at least two,has an edge which does not lie in any other clique of G and is clique reducible if it is not clique irreducible. A graph G is clique vertex irreducible if every clique in G has a vertex which does not lie in any other clique of G and clique vertex reducible if it is not clique vertex irreducible. The clique vertex irreducibility and clique irreducibility of graphs which are non-complete extended p-sums (NEPS) of two graphs are studied. We prove that if G(c) has at least two non-trivial components then G is clique vertex reducible and if it has at least three non-trivial components then G is clique reducible. The cographs and the distance hereditary graphs which are clique vertex irreducible and clique irreducible are also recursively characterized.

Studies on the Spectrum and the Energy of Graphs

Department of Mathematics, Cochin University of Science and Technology

An Approach Towards The Development Of An Efficient Symmetric Key Encryption Scheme

n the recent years protection of information in digital form is becoming more important. Image and video encryption has applications in various fields including Internet communications, multimedia systems, medical imaging, Tele-medicine and military communications. During storage as well as in transmission, the multimedia information is being exposed to unauthorized entities unless otherwise adequate security measures are built around the information system. There are many kinds of security threats during the transmission of vital classified information through insecure communication channels. Various encryption schemes are available today to deal with information security issues. Data encryption is widely used to protect sensitive data against the security threat in the form of “attack on confidentiality”. Secure transmission of information through insecure communication channels also requires encryption at the sending side and decryption at the receiving side. Encryption of large text message and image takes time before they can be transmitted, causing considerable delay in successive transmission of information in real-time. In order to minimize the latency, efficient encryption algorithms are needed. An encryption procedure with adequate security and high throughput is sought in multimedia encryption applications. Traditional symmetric key block ciphers like Data Encryption Standard (DES), Advanced Encryption Standard (AES) and Escrowed Encryption Standard (EES) are not efficient when the data size is large. With the availability of fast computing tools and communication networks at relatively lower costs today, these encryption standards appear to be not as fast as one would like. High throughput encryption and decryption are becoming increasingly important in the area of high-speed networking. Fast encryption algorithms are needed in these days for high-speed secure communication of multimedia data. It has been shown that public key algorithms are not a substitute for symmetric-key algorithms. Public key algorithms are slow, whereas symmetric key algorithms generally run much faster. Also, public key systems are vulnerable to chosen plaintext attack. In this research work, a fast symmetric key encryption scheme, entitled “Matrix Array Symmetric Key (MASK) encryption” based on matrix and array manipulations has been conceived and developed. Fast conversion has been achieved with the use of matrix table look-up substitution, array based transposition and circular shift operations that are performed in the algorithm. MASK encryption is a new concept in symmetric key cryptography. It employs matrix and array manipulation technique using secret information and data values. It is a block cipher operated on plain text message (or image) blocks of 128 bits using a secret key of size 128 bits producing cipher text message (or cipher image) blocks of the same size. This cipher has two advantages over traditional ciphers. First, the encryption and decryption procedures are much simpler, and consequently, much faster. Second, the key avalanche effect produced in the ciphertext output is better than that of AES.

On infinite graphs and related matrices

This thesis Entitled On Infinite graphs and related matrices.ln the last two decades (iraph theory has captured wide attraction as a Mathematical model for any system involving a binary relation. The theory is intimately related to many other branches of Mathematics including Matrix Theory Group theory. Probability. Topology and Combinatorics . and has applications in many other disciplines..Any sort of study on infinite graphs naturally involves an attempt to extend the well known results on the much familiar finite graphs. A graph is completely determined by either its adjacencies or its incidences. A matrix can convey this information completely. This makes a proper labelling of the vertices. edges and any other elements considered, an inevitable process. Many types of labelling of finite graphs as Cordial labelling, Egyptian labelling, Arithmetic labeling and Magical labelling are available in the literature. The number of matrices associated with a finite graph are too many For a study ofthis type to be exhaustive. A large number of theorems have been established by various authors for finite matrices. The extension of these results to infinite matrices associated with infinite graphs is neither obvious nor always possible due to convergence problems. In this thesis our attempt is to obtain theorems of a similar nature on infinite graphs and infinite matrices. We consider the three most commonly used matrices or operators, namely, the adjacency matrix

‘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