This repository contains homework assignments for the "Graph Algorithms and Networks" course at the University of Tehran, completed in the fall of 2021. The assignments are written in Persian and compiled using LaTeX.

This repository includes the following files and directories:

• HW1.tex: The LaTeX source file for the first homework assignment.
• HW2.tex: The LaTeX source file for the second homework assignment.
• Photos/: A directory containing images used in the homework assignments.
• neurips.sty, kbordermatrix.sty: LaTeX style files used for formatting the documents.
• XB Yas*.ttf: The Persian font files required to compile the documents.
• LICENSE: The license for this repository.
• .gitignore: A file specifying which files and directories to ignore in Git.

This assignment covers fundamental concepts of graph theory, including:

• Graph Properties: Calculating in-degrees and out-degrees of vertices.
• Graph Representation: Creating adjacency lists for given graphs.
• Paths and Cycles: Finding paths and identifying cycles in graphs.
• Graph-level Properties: Determining if graphs are acyclic, bipartite, or strongly connected.
• Minimum Spanning Trees: Finding the Minimum Spanning Tree (MST) of a graph using Kruskal's algorithm.

This assignment delves into more advanced graph algorithms:

• Matrix Representations: Creating node-arc incidence and node-node adjacency matrices.
• Network Flow: Modifying graphs to handle negative costs, arc capacities, and non-zero lower bounds.
• Graph Traversal: Performing Breadth-First Search (BFS) and Depth-First Search (DFS) and generating the corresponding trees.
• Topological Sorting: Finding a topological sort of a directed acyclic graph.
• Shortest Path: Applying Dijkstra's algorithm to find the shortest paths from a single source.

To compile the .tex files and generate PDFs of the homework assignments, you will need a working LaTeX distribution that supports XeLaTeX. TeX Live is recommended.

• LaTeX Distribution: TeX Live, MiKTeX, or MacTeX.
• xepersian package: This package is essential for compiling LaTeX documents with Persian text. It is included in most modern TeX distributions.
• XB Yas font: The font files are included in this repository. Ensure they are accessible to your LaTeX distribution, either by placing them in the same directory as the .tex files or by installing them on your system.

1. Clone the repository:

   git clone https://github.com/your-username/Graph-Algorithms-Fall2021.git
   cd Graph-Algorithms-Fall2021

2. Compile with xelatex: To compile the homework files, use the xelatex command. For example, to compile HW1.tex:

   xelatex HW1.tex

   You may need to run the command twice to ensure all cross-references are correctly updated.

This will produce a HW1.pdf file in the same directory. Repeat the process for HW2.tex.

This project is licensed under the MIT License - see the LICENSE file for details.