graph theory
TRANSCRIPT
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Solution of System of Linear and Non Linear Equations
Using Graph Theory
Team Members:Amar Chand : 13112009Deeksha Adlakha : 13112028
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What is Graph Theory?
Graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.
V = {a, b, c, d, e}E = {ab, ac, bd, cd, de}
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Applications of Graph Theory
• Computer Science
• Electrical Engineering
• Chemical Science
• General
• Other
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Types of Graphs
Null Graph Trivial Graph
• a
Non-Directed GraphDirected Graph
Simple Graph
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Connected Graph Disconnected Graph
Regular Graph Complete Graph
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Laplacian matrix
A simple graph G with n vertices, its Laplacian matrix L is defined as :
L = D - Awhere D is the degree matrix A is the adjacency matrix of the graph.
The elements of L are given by :
where Deg(Vi) is degree of the vertex i.
Li,j =
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Example :-
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Methods for solving a system of equations
Linear Equations: 1. Gaussian Elimination Method2. Gauss Jordan Elimination Method3. Gauss Seidel Method
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Non Linear Equations:1. Newton’s Method2. Secant Method
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Gaussian Elimination Method
Algorithm for solving system of linearequations (Ax=b) by bringing the augmented matrix to an upper triangular form.
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Example
Solve the following system of linear equations to obtain the values of x,y,z using Gaussian Elimination Method .
x – 3y +z = 42x – 8y + 8z = -2-6x + 3y – 15z = 9
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C++ Code
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