terryfields said:just need 2 definitions without proof for an exam tomorrow, don't need to use them for anything just need to be able to quote them but can't find them anyway so if someone could helpfully write them down that would be great
1)simple graph
2)connected graph
cheers
A simple graph is an undirected graph that does not contain any loops or multiple edges between the same pair of vertices. In other words, there is only one edge connecting any two given vertices in a simple graph.
A connected graph is a graph in which there is a path between every pair of vertices. This means that every vertex in the graph is connected to every other vertex in some way.
The main difference between a simple graph and a connected graph is that while a simple graph does not allow for loops or multiple edges, a connected graph requires that there is a path between every pair of vertices. In other words, a simple graph can have isolated vertices, while a connected graph cannot.
To determine if a graph is simple and connected, you can first check if there are any loops or multiple edges between the same pair of vertices. If there are none, then the graph is simple. To check if it is also connected, you can use a graph traversal algorithm, such as depth-first search or breadth-first search, to see if there is a path between every pair of vertices.
Simple and connected graphs are important in graph theory because they serve as the foundation for many other types of graphs and graph algorithms. They are also used to model real-world networks and systems, making them essential for understanding and solving problems in various fields such as computer science, mathematics, and social sciences.