Discrete Structures: Graphs & Trees
Discrete Structures: Graphs & Trees refers to fundamental mathematical concepts used in computer science and related fields. Graphs are collections of nodes connected by edges, representing relationships or networks, while trees are a special type of graph with a hierarchical, non-cyclic structure. Both are essential for modeling data, solving problems like searching and sorting, and underpinning algorithms in areas such as networking, databases, and artificial intelligence.
Discrete Structures: Graphs & Trees
Discrete Structures: Graphs & Trees refers to fundamental mathematical concepts used in computer science and related fields. Graphs are collections of nodes connected by edges, representing relationships or networks, while trees are a special type of graph with a hierarchical, non-cyclic structure. Both are essential for modeling data, solving problems like searching and sorting, and underpinning algorithms in areas such as networking, databases, and artificial intelligence.
💡 Key Takeaways
- Define graphs: vertices and edges; distinguish between undirected and directed graphs.
- Describe trees as connected, acyclic graphs with a hierarchical structure (roots, leaves).
- Explore core properties: degree, paths, cycles, connectivity; note trees have n-1 edges.
- Learn basic traversals (DFS and BFS) for exploring graphs and trees and solving search problems.
- Recognize real-world applications in networks, data structures, parsing, and optimization.
❓ Frequently Asked Questions
What is a graph?
A graph is a set of vertices (nodes) connected by edges. Edges can be undirected or directed, and graphs model relationships or networks.
What is a tree?
A tree is a connected acyclic graph. It has n vertices and n−1 edges, and there is a unique simple path between any two vertices.
What is the difference between directed and undirected graphs?
In an undirected graph, edges have no direction. In a directed graph (digraph), edges have a direction from one vertex to another, creating in-degrees and out-degrees.
What is a spanning tree?
A spanning tree is a subgraph that connects all vertices and is a tree. It has exactly n−1 edges; in a weighted graph, a minimum spanning tree minimizes the total edge weight.