Graphs, trees, and basic graph properties and terminology from an intro discrete mathematics course.
35 cards · basic cards · AI-written, checked twice. Edit anything.
- What is a graph?
- A mathematical structure consisting of vertices (nodes) and edges (connections) between them.
- What is a vertex in a graph?
- A fundamental unit of a graph, also called a node; the point where edges connect.
- What is an edge in a graph?
- A connection between two vertices (or a vertex and itself).
- Define a directed graph.
- A graph in which each edge has a direction, represented as an arrow pointing from one vertex to another.
- Define an undirected graph.
- A graph in which edges have no direction; the connection between two vertices is mutual.
- What is a weighted graph?
- A graph in which each edge has an associated numerical value, called its weight.
- Define the degree of a vertex.
- The number of edges incident to (connected to) that vertex.
- State the Handshaking Lemma.
- The sum of the degrees of all vertices equals twice the number of edges.
- What is a simple graph?
- An undirected graph with no loops and no multiple edges between the same pair of vertices.
- What is a multigraph?
- A graph in which multiple edges can connect the same pair of vertices.
- Define a loop in a graph.
- An edge that connects a vertex to itself.
- What is a connected graph?
- A graph in which there is a path between every pair of vertices.
- What is a disconnected graph?
- A graph in which at least one pair of vertices has no path between them.
- Define a connected component.
- A maximal connected subgraph of a graph; a subset where every vertex is reachable from every other vertex in that subset.
- What is a walk in a graph?
- A sequence of vertices in which each consecutive pair is connected by an edge; vertices and edges may repeat.