🌴Graph and Trees

Definitions and Basic Properties

• A graph is a collection of vertices (also called nodes) and edges (also called links) that connect pairs of vertices.

• Graphs can be directed (where edges have a direction) or undirected (where edges do not have a direction).

• The degree of a vertex in a graph is the number of edges incident to it.

• A tree is a connected, acyclic graph.

• Trees have many useful properties, such as the fact that any two vertices in a tree are connected by a unique path.

• Binary trees are trees where each node has at most two children.

• Trees can be used to model hierarchical relationships, such as family trees or organizational charts.

• Spanning trees are trees that include all the vertices of a graph.

Spanning Trees

The spanning trees are trees that include all the vertices of a graph.

• Finding spanning trees using depth-first search and breadth-first search algorithms

DFS and BFS can be used to find spanning trees in a graph