Clique Irreducibility of Some Iterative Classes of Graphs

In this paper, two notions, the clique irreducibility and clique vertex irreducibility are discussed. A graph 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 it is clique vertex irreducible if every clique in G has a vertex which does not lie in any other clique of G. It is proved that L(G) is clique irreducible if and only if every triangle in G has a vertex of degree two. The conditions for the iterations of line graph, the Gallai graphs, the anti-Gallai graphs and its iterations to be clique irreducible and clique vertex irreducible are also obtained.

Some classes of Turker equivalent graphs

Two graphs G and H are Turker equivalent if they have the same set of Turker angles. In this paper some Turker equivalent family of graphs are obtained.

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

Studies on Some Graph Classes

Department of Mathematics, Cochin University of Science and Technology

Self-assembled Transition Metal Coordination Frameworks of Carbohydrazone and Thiocarbohydrazone Ligands: Structural, Spectral, Magnetic and Anticancer Properties

Chemistry occupies a unique middle position in the scientific arena, between physics and mathematics on the one side and biology, ecology, sociology and economics on the other [1]. Chemistry is the science of matter and of its transformations, and life is its highest expression [2]. According to reductionist thinking biology is reducible into chemistry, chemistry into physics, and ultimately physics into mathematics. Reductionism implies the ease of understanding one level in terms of another.The work presented this thesis comprises synthesis and characterization of suitably substituted thiocarbohydrazone and carbohydrazone ligand building blocks, self-assembled metallosupramolecular square grid complexes as well as some di/multinuclear complexes. The primary aim was the deliberate syntheses of some novel transition metal framework complexes, mainly metallosupramolecular coordination square grids by self-assembly and their physico-chemical characterization. The work presented, however, also include synthesis and characterization of four mononuclear Ni(II) complexes of two thiosemicarbazones, which we carried out as a preliminary and supporting study. Based on the present work we would like to conclude that the carbohydrazones, thiocarbohydrazones and their coordination framework complexes of transition metals are promising systems for wide application in science and technology varied from physics to biotechnology. Novel classes of materials and biologically important potential compounds open up further scope of researches and we hopefully welcome any sort of related research to make this work more valuable.

Rainfall Climatology over Middle East Region and its Variability

A better understanding of the rainfall climatology of the Middle East region identifying the mechanisms responsible for the rain producing systems is essential for effective utilization of the water resources over the arid region. A comprehensive analysis on the rainfall climatology of the Middle East region is carried out to bring out the spatial and temporal variation of rainfall and mechanisms responsible for the rain events. The study was carried out utilizing rainfall, OLR, wind and humidity data sets procured from TRMM, NOAA and NCEP-NCAR. Climatology of annual rainfall brings out two areas of alarmingly low rainfall in the Middle East region: one in Egypt, Jordan and adjoining areas and the other in the southern part of Saudi Arabia. Daily rainfall analysis indicates that northern region gets rainfall mainly during winter and spring associated with the passage of Mediterranean low pressure systems whereas rain over the southern region is caused mainly by the monsoon organized convection, cross equatorial flow and remnants of low pressure systems associated with the monsoon during the summer season. Thermodynamic structure of the atmosphere reveals that the region does not have frequent local convection due to insufficient moisture content. The sinking motion associated with the sub tropic high pressure system and subsidence associated with the Walker circulation are responsible for maintaining warm and dry air over the region.

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.

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

Fair Sets of Some Classes of Graphs

Given a non empty set S of vertices of a graph, the partiality of a vertex with respect to S is the di erence between maximum and minimum of the distances of the vertex to the vertices of S. The vertices with minimum partiality constitute the fair center of the set. Any vertex set which is the fair center of some set of vertices is called a fair set. In this paper we prove that the induced subgraph of any fair set is connected in the case of trees and characterise block graphs as the class of chordal graphs for which the induced subgraph of all fair sets are connected. The fair sets of Kn, Km;n, Kn e, wheel graphs, odd cycles and symmetric even graphs are identi ed. The fair sets of the Cartesian product graphs are also discussed

Content Based Image Retrieval of Brain MR Images across Different Classes

Magnetic Resonance Imaging play a vital role in the decision-diagnosis process of brain MR images. For an accurate diagnosis of brain related problems, the experts mostly compares both T1 and T2 weighted images as the information presented in these two images are complementary. In this paper, rotational and translational invariant form of Local binary Pattern (LBP) with additional gray scale information is used to retrieve similar slices of T1 weighted images from T2 weighted images or vice versa. The incorporation of additional gray scale information on LBP can extract more local texture information. The accuracy of retrieval can be improved by extracting moment features of LBP and reweighting the features based on users’ feedback. Here retrieval is done in a single subject scenario where similar images of a particular subject at a particular level are retrieved, and multiple subjects scenario where relevant images at a particular level across the subjects are retrieved