A Semi-Total Domination Number of a Graph

This thesis work on the two parameters that is very important domination parameters, one parameter is known as domination number and other parameter is called as total domination number. S is defined as a set of vertices in a graph G. We characterize a set S of vertices in a graph G with no segregated vertices to be a semitotal overwhelming arrangement of G in the event that it is a ruling arrangement of G and furthermore every vertex in S is inside separation 2 of another vertex of S. The semitotal domination number, indicated by is the base cardinality of a semitotal ruling arrangement of G. We demonstrate that on the off chance that G is an associated graph on n ? 4 vertices, at that point and we describe the trees and diagrams of least degree 2 arriving at this bound

Triple Connected Domination Number of Graph

The concept of triple connected graphs with real life application was prefaced by considering the existence of a path containing any three vertices of a graph G. In this paper, we introduce a new domination parameter, called triple connected domination number of a graph. A subset S of V of a nontrivial graph G is said to be triple connected dominating set, if S is a dominating set and the induced sub graph is triple connected. The minimum cardinality undertake all triple connected dominating sets. Then which is called the triple connected domination number and is denoted by ?tc

Fixed Point Theorem of Generalized Contradiction in Partially Ordered Cone Metric Spaces

In this thesis we discuss the newly introduced concept of cone metric spaces, prove some fixed point theorems existence results of contractive mappings defined on such cone metric space and improve some well-known results in the normal case. The purpose of this paper is to establish the generalization of contractive type mappings on complete cone metric spaces. Also all the results in this paper are new. The main aim of this paper is to prove fixed point theorems is cone metric spaces which extend the Banach contraction mapping and others. This is achieved by introducing different kinds of Cauchy sequences in cone metric spaces

The Fundamental Group on Algebraic Topology

Algebraic topology is mostly about finding invariants for topological spaces. The fundamental group is the simplest, in some ways, and the most difficult in others. This project studies the fundamental group, its basic properties, some elementary computations, and a resulting theorem. In this paper, we will examine the construction and nature of the first homotopy group, which is more commonly known as the fundamental group of a topological space. We will first briefly cover the basics of point-set topology, then use these concepts to facilitate a rigorous study of the construction of the fundamental group

A Study on Graph Theory of Path Graphs

A simple graph G = (V, E) consists of V , a nonempty set of vertices, and E, a set of unordered pairs of distinct elements of V called edges. Simple graphs have their limits in modeling the real world. Instead, we use multigraphs, which consist of vertices and undirected edges between these vertices, with multiple edges between pairs of vertices allowed. In the mathematical field of graph theory, a path graph or linear graph is a graph whose vertices can be listed in the order v1, v2, …, vn such that the edges are {vi, vi+1} where i = 1, 2, …, n ? 1. Equivalently, a path with at least two vertices is connected and has two terminal vertices (vertices that have degree 1), while all others (if any) have degree 2. Paths are often important in their role as subgraphs of other graphs, in which case they are called paths in that graph. A path is a particularly simple example of a tree, and in fact the paths are exactly the trees in which no vertex has degree 3 or more. A disjoint union of paths is called a linear forest

A Study on Combinatories in Discrete Mathematics

The next two chapters deal with Set Theory and some related topics from Discrete Mathematics. This chapter develops the basic theory of sets and then explores its connection with combinatorics (adding and multiplying; counting permutations and combinations), while Chapter 5 treats the basic notions of numerosity or cardinality for finite and infinite sets.Most mathematicians today accept Set Theory as an adequate theoretical foundation for all of mathematics, even as the gold standard for foundations.* We will not delve very deeply into this aspect of Set Theory or evaluate the validity of the claim, though we will make a few observations on it as we proceed. Toward the end of our treatment, we will focus on how and why Set Theory has been axiomatized. But even disregarding the foundational significance of Set Theory, its ideas and terminology have become indispensable for a large number of branches of mathematics as well as other disciplines, including parts of computer science. This alone makes it worth exploring in an introductory study of Discrete Mathematics

Minimizing End-to-End Delay and Maximizing Reliability using Multilayer Neural Network-based Hamming Back Propagation for Efficient Communication in WSN

Wireless sensor network (WSN) comprises number of spatially distributed sensor nodes for monitoring the physical environment conditions and arranging the gathered data at central location. WSN gained large attention in medical field, industry, military, etc. However, congestion control mechanism for communication between sensor nodes failed to consider the end-to-end delay features. In addition, it failed to handle reliability and not achieved the data concurrency. In order to address the above mentioned problems, Multilayer Neural Network-based Hamming Back Propagation (MNN-HBP) technique is introduced for efficient communication in WSN. In MNN-HBP technique, Amorphous View Point Algorithm is introduced for sensor node initialization for efficient communication in WSN. Amorphous View Point Algorithm used time of arrival to measure the time distance between the sender node and receiver node. After that Hamming Back Propagation Algorithm is used to identify the current location of the sensor nodes for minimizing the end-to end delay and improving the reliability. Each sensor node compares their distance with the neighbouring sensor nodes distance to identify the associated error. When the distance is higher, the associated error is higher and propagates error back to other sensor nodes in the previous layers. The process gets repeated until the communication established between source sensor and lower associated error nodes. By this way, efficient communication is carried out with higher reliability and minimum end-to end delay. Extensive simulation are conducted to illustrate the efficiency of proposed technique as well as the impacts of network parameters on end-to-end delay, reliability and data packets successful rate with respect to data packet size and number of data packets

Financial Analysis of “Corporation Bank” with Special Reference to Coimbatore, Tamilnadu

Financial analysis of an organization provides the clear view of its performance parameters, present as well as past performance. This analysis is important for the management and also for outsiders dealing with organization as this shows the way of functioning and the direction in which an organization is moving. It is helpful in assessing the corporate excellence, judging the credit worthiness, processing bond rating and assessing market risk. The main study is to find out the financial performance of the bank. The ratio analysis and interpretation can provide valuable insights into a bank’s performance. Keywords: 1. Financial Management: “Financial management is concerned with the efficient use of an important economic resource, namely, capital funds. 2. Financial Analysis: Financial analysis refers to an assessment of the viability, stability and profitability of a business sub-business or project. 3. Trend Analysis: Trend Analysis is the practice of collecting information and attempting to spot a pattern, or trend, in the information

DOMINATION AND EDGE DOMINATION IN TREES

Let $G=(V,E)$ be a simple graph. A set $S\subseteq V$ is a dominating set if every vertex in $V \setminus S$ is adjacent to a vertex in $S$. The domination number of a graph $G$, denoted by $\gamma(G)$ is the minimum cardinality of a dominating set of $G$. A set $D \subseteq E$ is an edge dominating set if every edge in $E\setminus D$ is adjacent to an edge in $D$. The edge domination number of a graph $G$, denoted by $\gamma'(G)$ is the minimum cardinality of an edge dominating set of $G$. We characterize trees with  domination number equal to twice edge domination number

Antimicrobial activity of Aegle marmelos against clinical pathogens

Aegle marmelos is a medicinal herb belongs to the family Rutaceae. The different parts of plants like leaves and flowers are extracted by using the solvent methanol. The methanol extracts were screened for the antimicrobial activity. They showed greater inhibitory effect against both gram positive and gram negative organisms. The organisms used were such as Escherichia coli, Pseudomonas aeruginosa, Proteus mirabilis, Salmonella typhi, Staphylococcus aureus. Based on the present investigation results it is concluded that the methanolic extracts of Aegle marmelos has great potential as antimicrobial agent against different microorganisms and they can be used in the treatment of infections diseases caused by the resistant microorganisms