Studies on Some Graph Classes

Department of Mathematics, Cochin University of Science and Technology

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

Department of Mathematics, Cochin University of Science and Technology

Measurement and simulation of anisotropy in the Infrared and Raman spectra of beta-FeSi2 single crystals

In this paper we show that the orthorhombic phase of FeSi2 (stable at room temperature) displays a sizable anisotropy in the infrared spectra, with minor effects in the Raman data too. This fact is not trivial at all, since the crystal structure corresponds to a moderate distortion of the fluorite symmetry. Our analysis is carried out on small single crystals grown by flux transport, through polarization-resolved far-infrared reflectivity and Raman measurements. Their interpretation has been obtained by means of the simulated spectra with tight-binding molecular dynamics.

Strongly distance-balanced graphs and graph products

A graph G is strongly distance-balanced if for every edge uv of G and every i 0 the number of vertices x with d.x; u/ D d.x; v/ 1 D i equals the number of vertices y with d.y; v/ D d.y; u/ 1 D i. It is proved that the strong product of graphs is strongly distance-balanced if and only if both factors are strongly distance-balanced. It is also proved that connected components of the direct product of two bipartite graphs are strongly distancebalanced if and only if both factors are strongly distance-balanced. Additionally, a new characterization of distance-balanced graphs and an algorithm of time complexity O.mn/ for their recognition, wheremis the number of edges and n the number of vertices of the graph in question, are given

Median Sets and Median Number of a Graph

A profile is a finite sequence of vertices of a graph. The set of all vertices of the graph which minimises the sum of the distances to the vertices of the profile is the median of the profile. Any subset of the vertex set such that it is the median of some profile is called a median set. The number of median sets of a graph is defined to be the median number of the graph. In this paper, we identify the median sets of various classes of graphs such as Kp − e, Kp,q forP > 2, and wheel graph and so forth. The median numbers of these graphs and hypercubes are found out, and an upper bound for the median number of even cycles is established.We also express the median number of a product graph in terms of the median number of their factors.

On The Center Sets and Center Numbers of Some Graph Classes

For a set S of vertices and the vertex v in a connected graph G, max x2S d(x, v) is called the S-eccentricity of v in G. The set of vertices with minimum S-eccentricity is called the S-center of G. Any set A of vertices of G such that A is an S-center for some set S of vertices of G is called a center set. We identify the center sets of certain classes of graphs namely, Block graphs, Km,n, Kn −e, wheel graphs, odd cycles and symmetric even graphs and enumerate them for many of these graph classes. We also introduce the concept of center number which is defined as the number of distinct center sets of a graph and determine the center number of some graph classes

Raman spectra of KTP crystal in an in situ electric field

Raman spectra of the KTP single crystal are recorded in electric fields (dc and ac) applied along the polar axis c. Spectra with the laser beam focused near the cathode end, anode end and the centre of the crystal are recorded. The cathode end of the crystal develops a spot ‘grey track’ where the laser beam is focused after a lapse of 5 h from the application of a dc electric field of 38 V/cm. The spectra recorded at the cathode end after the application of field show variations in intensity of bands. A new band appears at 177 cm21. Changes in band intensities are explained on the basis of changes in polarizability of the crystal due to the movement of K1 ions along the polar axis. K1 ions accumulate at the cathode end, where the ‘Grey track’ formation occurs. The intensity enhancement observed for almost all bands in the ac field is attributed to the improvement of crystalline quality.

Infrared and polarized Raman spectra of Cu(HSeO3)2 • H20 single crystal

Infrared and polarized Raman spectra of Cu(HSeO3) 2 - H20 single crystal have been recorded and analysed. The appearance of non-degenerate Se-OH stretching vibrations in the ~x: and ~y: polarizations of Raman spectra indicate distortion of the HSeO~- ion in the Cu(HSeO3)2 - H20 crystal. The low wavenumber values obtained for the symmetric and asymmetric stretching vibrations of the HSeO 3 ion are consistent with the strong hydrogen bonding and the influence of Jahn-Teller distortion as predicted in X-ray diffraction data. The shifting of the stretching and bending vibrations of the hydroxyl groups and water molecules from the free state values also confirms the strong hydrogen bonding in this crystal. Broad bands observed for both stretching and bending regions become sharp in the Raman spectrum recorded at 77 K. A doublet appears for the Se-OH stretching mode at this temperature indicating the settling of protons in an ordered position and the absence of intrabond proton tunnelling

Raman and FTIR spectra of [Cu(H2O)6](BrO3)2 and [Al(H2O)6](BrO3)3 · 3H2O

Raman and FTIR spectra of [Cu(H2O)6](BrO3)2 and [Al(H2O)6](BrO3)3 · 3H2O are recorded and analyzed. The observed bands are assigned on the basis of BrO3 − and H2O vibrations. Additional bands obtained in the region of 3 and 1 modes in [Cu(H2O)6](BrO3)2 are due to the lifting of degeneracy of 3 modes, since the BrO3 − ion occupies a site of lower symmetry. The appearance 1 mode of BrO3 − anion at a lower wavenumber (771 cm−1) is attributed to the attachment of hydrogen to the BrO3 − anion. The presence of three inequivalent bromate groups in the [Al(H2O)6](BrO3)3 · 3H2O structure is confirmed. The lifting of degeneracy of 4 mode indicates that the symmetry of BrO3 − anion is lowered in the above crystal from C3v to C1. The appearance of additional bands in the stretching and bonding mode regions of water indicates the presence of hydrogen bonds of different strengths in both the crystals. Temperature dependent Raman spectra of single crystal [Cu(H2O)6](BrO3)2 are recorded in the range 77–523 K for various temperatures. A small structural rearrangement takes place in BrO3 − ion in the crystal at 391 K. Hydrogen bounds in the crystal are rearranging themselves leading to the loss of one water molecule at 485 K. This is preceded by the reorientation of BrO3 − ions causing a phase transition at 447 K. Changes in intensities and wavenumbers of the bands and the narrowing down of the bands at 77 K are attributed to the settling down of protons into ordered positions in the crystal

Temperature dependent polarized Raman spectra of nonaaqualanthanoid (Pr) single crystal

Polarized Raman spectral changes with respect to temperature were investigated for Pr(BrO3)3·9H2O single crystals. FTIR spectra of hydrated and deuterated analogues were also recorded and analysed. Temperature dependent Raman spectral variation have been explained with the help of the thermograms recorded for the crystal. Factor group analysis could propose the appearance ofBrO3 ions at sites corresponding to C3v (4) and D3h (2). Analysis of the vibrational bands at room temperature confirms a distorted C3v symmetry for the BrO3 ion in the crystal. From the vibrations of water molecules, hydrogen bonds of varying strengths have also been identified in the crystal. The appearance υ1 mode of BrO3− anion at lower wavenumber region is attributed to the attachment of hydrogen atoms to the BrO3− anion. At high temperatures, structural rearrangement is taking place for bothH2Omolecule and BrO3 ions leading to the loss ofwater molecules and structural reorientation of bromate ions causing phase transition of the crystal at the temperature of 447 K.

X-Ray spectra of superheavy and quasi-superheavy elements

We discuss the possibility of identifying superheavy elements from the observation of their M-shell x-ray spectra, which might occur during the collision of a superheavy element with a heavy target. The same question is discussed for the possible observation of the x-rays from the quasimolecule (quasi-superheavy element) which is formed during such a heavy-ion collision. It is shown that it is very difficult, if not impossible, to determine any information about the interesting quantum electrodynamical effects from the M-shell x-ray spectra of these quasimolecules.

Interchannel interactions and relaxation in the 2p auger spectra of Mg-like ions

Relativistic Auger rates for the 2p spectra of Mg-like ions have been calculated in the atomic range 13 < Z < 36. We used the multiconfiguration Dirac-Fock method but beyond a simple frozen-orbital approach we include also relaxation for the bound electrons and the interchannel interaction between the continuum states. Both effects may alter the individual transition rates remarkably. This is analysed for a few selected states within the isoelectronic sequence. Weak transitions within the 2p spectra can be changed by an order of magnitude because of the continuum coupling. The influence of both effects for higher-Z ions is reduced but still remain visible.

Content aggregation on knowledge bases using graph clustering

Recently, research projects such as PADLR and SWAP have developed tools like Edutella or Bibster, which are targeted at establishing peer-to-peer knowledge management (P2PKM) systems. In such a system, it is necessary to obtain provide brief semantic descriptions of peers, so that routing algorithms or matchmaking processes can make decisions about which communities peers should belong to, or to which peers a given query should be forwarded. This paper proposes the use of graph clustering techniques on knowledge bases for that purpose. Using this clustering, we can show that our strategy requires up to 58% fewer queries than the baselines to yield full recall in a bibliographic P2PKM scenario.