Graph theory
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Transcript of Graph theory
Solution of System of Linear and Non Linear Equations
Using Graph Theory
Team Members:Amar Chand : 13112009Deeksha Adlakha : 13112028
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}
Applications of Graph Theory
• Computer Science
• Electrical Engineering
• Chemical Science
• General
• Other
Types of Graphs
Null Graph Trivial Graph
• a
Non-Directed GraphDirected Graph
Simple Graph
Connected Graph Disconnected Graph
Regular Graph Complete Graph
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 =
Example :-
Methods for solving a system of equations
Linear Equations: 1. Gaussian Elimination Method2. Gauss Jordan Elimination Method3. Gauss Seidel Method
Non Linear Equations:1. Newton’s Method2. Secant Method
Gaussian Elimination Method
Algorithm for solving system of linearequations (Ax=b) by bringing the augmented matrix to an upper triangular form.
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
C++ Code
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