Discrete Math for Computer Science, unit: Graph Theory. Core concepts, terminology, and worked-example cues a college student meets for this unit, building on prior units without repeating them. Front: a term, concept, or short problem cue. Back: the definition, explanation, or answer.
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- What is a graph, in discrete mathematics?
- A structure consisting of vertices (nodes) connected by edges
- What is a vertex, in graph theory?
- A fundamental unit (node or point) of a graph
- What is an edge, in graph theory?
- A connection between two vertices in a graph
- What is a directed graph?
- A graph where edges have a specific direction from one vertex to another
- What is an undirected graph?
- A graph where edges have no direction, representing a mutual connection
- What is the degree of a vertex?
- The number of edges connected to that vertex
- What is a path, in graph theory?
- A sequence of edges connecting a sequence of distinct vertices
- What is a cycle, in graph theory?
- A path that starts and ends at the same vertex without repeating other vertices
- What is a connected graph?
- A graph where there is a path between every pair of vertices
- What is a weighted graph?
- A graph where each edge has an associated numerical value, often representing cost or distance
- What is a tree, in graph theory?
- A connected, acyclic graph
- What is a bipartite graph?
- A graph whose vertices can be divided into two sets with edges only between the sets, never within
- What is a complete graph?
- A graph where every pair of vertices is connected by an edge
- What is graph coloring?
- Assigning labels (colors) to vertices so no two adjacent vertices share the same color
- What is an adjacency matrix?
- A matrix representation of a graph showing which vertex pairs are connected
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