# User:Vitalij zad/Sandbox

{{Reading level}} **Graph Theory** is the study of nodes and the edges connecting those nodes, and topics such as combinatorics, networks, scheduling, and connectivity. Graph theory does not examine graphs as in Calculus (curves and other related concepts). Graph theory can be thought of as the "mathematician's connect-the-dots".

## What is Graph Theory?

- Graph Theory (graph theory) is the study of interactions between nodes (vertices) and edges (connections between the vertices).
- There are many applications of graph theory to mathematics, combinatorics, computer science and programming, engineering, networks and relationships, scheduling, and many more.

## What is a Graph?

In contrast to the common knowledge of graph as a line or curve drawn on the cartesian(x,y) or radial(r,theta) axes, in the context of graph thery, a **Graph** G=(V,E) consists of a set V of vertices and another set E of edges whose relation is defined by an unordered pair of vertices (v_{i},v_{j}) related to an edge e_{k}. The graphical representation of a graph can be done in various ways, the most common way being representation of vertices as dots and edges as lines connecting them. Graphs are used in diverse fields, computer networks being one of them.

## Graph Definitions

- Nodes and Edges
- Traversals and Paths
- Connectivity
- Independence
- Isomorphic
- Complement graphs
- Trees
- Complete graphs
- Bipartite graphs
- New graphs from old ones
- Types of graphs

## Simple Tools

- Juggling with Binomial Coefficients
- Dual Graphs
- Star-Delta and Similar Transformations
- Hypercubes and Gray Codes

## Degrees and Parameters

- Degree Definitions
- Theorems using Degrees
- Regular Graphs
- Degree Sequences
- Using matrices to encode graphs

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