Studies on the Spectrum and the Energy of Graphs

Department of Mathematics, Cochin University of Science and Technology

Betweenness Centrality in Some Classes of Graphs

There are several centrality measures that have been introduced and studied for real world networks. They account for the different vertex characteristics that permit them to be ranked in order of importance in the network. Betweenness centrality is a measure of the influence of a vertex over the flow of information between every pair of vertices under the assumption that information primarily flows over the shortest path between them. In this paper we present betweenness centrality of some important classes of graphs.

Finite size effects on the structural and magnetic properties of sol–gel synthesized NiFe2O4 powders

Nanoparticles of nickel ferrite have been synthesized by the sol–gel method and the effect of grain size on its structural and magnetic properties have been studied in detail. X-ray diffraction (XRD) studies revealed that all the samples are single phasic possessing the inverse spinel structure. Grain size of the sol–gel synthesized powders has been determined from the XRD data and the strain graph. A grain size of 9 nm was observed for the as prepared powders of NiFe2O4 obtained through the sol–gel method. It was also observed that strain was induced during the firing process. Magnetization measurements have been carried out on all the samples prepared in the present series. It was found that the specific magnetization of the nanosized NiFe2O4 powders was lower than that of the corresponding coarse-grained counterparts and decreased with a decrease in grain size. The coercivity of the sol–gel synthesized NiFe2O4 nanoparticles attained a maximum value when the grain size was 15nm and then decreased as the grain size was increased further.

Towards the development of a new wavelet for ECG classification

In this paper an attempt has been made to determine the number of Premature Ventricular Contraction (PVC) cycles accurately from a given Electrocardiogram (ECG) using a wavelet constructed from multiple Gaussian functions. It is difficult to assess the ECGs of patients who are continuously monitored over a long period of time. Hence the proposed method of classification will be helpful to doctors to determine the severity of PVC in a patient. Principal Component Analysis (PCA) and a simple classifier have been used in addition to the specially developed wavelet transform. The proposed wavelet has been designed using multiple Gaussian functions which when summed up looks similar to that of a normal ECG. The number of Gaussians used depends on the number of peaks present in a normal ECG. The developed wavelet satisfied all the properties of a traditional continuous wavelet. The new wavelet was optimized using genetic algorithm (GA). ECG records from Massachusetts Institute of Technology-Beth Israel Hospital (MIT-BIH) database have been used for validation. Out of the 8694 ECG cycles used for evaluation, the classification algorithm responded with an accuracy of 97.77%. In order to compare the performance of the new wavelet, classification was also performed using the standard wavelets like morlet, meyer, bior3.9, db5, db3, sym3 and haar. The new wavelet outperforms the rest

A Study of Some Centrality Measures in Graphs

Centrality is in fact one of the fundamental notions in graph theory which has established its close connection with various other areas like Social networks, Flow networks, Facility location problems etc. Even though a plethora of centrality measures have been introduced from time to time, according to the changing demands, the term is not well defined and we can only give some common qualities that a centrality measure is expected to have. Nodes with high centrality scores are often more likely to be very powerful, indispensable, influential, easy propagators of information, significant in maintaining the cohesion of the group and are easily susceptible to anything that disseminate in the network.