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GRAPHICAL METHODS IN OPERATION RESEARCH

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  Linear Programming Linear programming is a mathematical technique employed to determine the most favorable solution for a problem characterized by linear relationships. It is a valuable tool in fields such as operations research, economics, and engineering, where efficient resource allocation and optimization are critical. Now let’s learn about types of linear programming problems Types of Linear Programming Problems There are mainly three types of problems based on Linear programming they are, Manufacturing Problem:  In this type of problem, some constraints like manpower, output units/hour, and machine hours are given in the form of a linear equation. And we have to find an optimal solution to make a maximum profit or minimum cost. Diet Problem:  These problems are generally easy to understand and have fewer variables. Our main objective in this kind of problem is to minimize the cost of diet and to keep a minimum amount of every constituent in the diet.  Transpo...
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INTRODUCTION TO STATISTICS

 UNIT 1 INTRODUCTION TO STATISTICS Structure 1.0 Introduction 1.1 Objectives 1.2 Meaning of Statistics 1.2.1 Statistics in Singular Sense 1.2.2 Statistics in Plural Sense 1.2.3 Definition of Statistics 1.3 Types of Statistics 1.3.1 On the Basis of Function 1.3.2 On the Basis of Distribution of Data 1.4 Scope and Use of Statistics 1.5 Limitations of Statistics 1.6 Distrust and Misuse of Statistics 1.7 Let Us Sum Up 1.8 Unit End Questions 1.9 Glossary 1.10 Suggested Readings 1.0 INTRODUCTION The word statistics has different meaning to different persons. Knowledge of statistics is applicable in day to day life in different ways. In daily life it means general calculation of items, in railway statistics means the number of trains operating, number of passenger’s freight etc. and so on. Thus statistics is used by people to take decision about the problems on the basis of different type of quantitative and qualitative information available to them. However, in behavioural sciences, the ...
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Spectral Graph Theory

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  Spectral graph theory 12 languages Article Talk Read Edit View history Tools From Wikipedia, the free encyclopedia In  mathematics ,  spectral  graph theory  is the study of the properties of a  graph  in relationship to the  characteristic polynomial ,  eigenvalues , and  eigenvectors  of matrices associated with the graph, such as its  adjacency matrix  or  Laplacian matrix . The adjacency matrix of a simple undirected graph is a  real   symmetric matrix  and is therefore  orthogonally diagonalizable ; its eigenvalues are real  algebraic integers . While the adjacency matrix depends on the vertex labeling, its  spectrum  is a  graph invariant , although not a complete one. Spectral graph theory is also concerned with graph parameters that are defined via multiplicities of eigenvalues of matrices associated to the graph, such as the  Colin de Verdière number . Cospectral...
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