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ACA Semester Long Project
Graphs
Introduction to Graphs: Theory and Algorithms
Introduction
Introduction
What are Graphs?
A collection of vertices and edges.
What can we do with graphs?
There is a lot of stuff that involve applications of Graph Theory. Simplest example being finding routes on maps.
We'll be exploring various aspects of graph theory during the course of this project.
Graph Colorings
Graph Colorings
- As the name suggests, we will color graphs.
- We can either color the vertices or the edges.
- There are interesting properties we will discover while doing this topic.
- Various scheduling problems can be modeled as graph coloring problems.
- Graph coloring approach can even be used to allocate spaces to variables in the processors.
Turan's Theorem/Cages/Ramsey Theory
- Also known as extremal problems.
- In these, we are interested in the extremes.
- We'll be looking at smallest or largest graphs satisfying a particular property.
Turan's Theorem/ Cages/Ramsey Theory
Countings and Labellings
- Counting is a very important topic in graphs as we are often interested in counting possibilities of graphs with certain properties.
- Labellings are stronger version of colorings of graphs, as in labellings we can use numbers, letters or any other symbol we like.
Countings and Labellings
Graph Algorithms
Graph Algorithms
- Searches
- Paths
- Spanning Trees
- Network Flows
- Coloring Algorithms
Other interesting Topics
Other interesting topics
- Drawing of Graphs
- Planarity of Graphs
- Heaps
- Maze generators
- Matchings
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