Handshaking Theorem Verification System

README

i. Short Intro

This project demonstrates the Handshaking Theorem using randomly generated graphs and adjacency matrices.

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ii. Used Technologies

• C Programming Language
• Dynamic Memory Allocation
• Adjacency Matrix
• Random Number Generation

Libraries Used

• stdio.h
• stdlib.h
• time.h

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iii. Features

User Can:

• Generate random graphs
• Enter custom vertices
• Calculate degree sums
• Verify Handshaking Theorem
• Measure execution time

Keyboard Inputs

Action	Input
Continue Program	y
Exit Program	n

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iv. The Process

1. Took vertex input from user.
2. Created adjacency matrix dynamically.
3. Generated random edges.
4. Calculated vertex degrees.
5. Verified:

[ \sum deg(v) = 2|E| ]

6. Measured execution time.

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v. What I Learned

• Graph representation
• Dynamic memory allocation
• Graph theory implementation
• Performance analysis

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vi. Future Improvements

• Graph visualization
• Weighted graph support
• Export graph data
• Better memory optimization

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vii. How to Run

Compile

gcc handshaking_theorem.c -o handshaking

Run

./handshaking