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Discrete Math - Graph Theory Basics
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Path
A sequence of vertices where each adjacent pair is connected by an edge.
Adjacency Matrix
A square matrix used to represent a finite graph, with rows and columns labeled by graph vertices.
Forest
A collection of trees.
Directed Graph (Digraph)
A graph in which the edges have a direction.
Adjacent Vertices
Two vertices are adjacent if they are connected by an edge.
Weighted Graph
A graph where edges have an associated weight or cost.
Hamiltonian Path
A path in a graph that visits each vertex exactly once.
Adjacent Edges
Two edges are adjacent if they share a common vertex.
Graph
A set of vertices connected by edges.
Bipartite Graph
A graph whose vertices can be divided into two disjoint sets such that no two vertices within the same set are adjacent.
Cycle
A path that starts and ends at the same vertex without traversing any other vertex more than once.
Subgraph
A graph formed from a subset of the vertices and edges of another graph.
Planar Graph
A graph that can be embedded in the plane, so no edges intersect except at their endpoints.
Tree
A connected graph with no cycles.
Vertex Cover
A set of vertices that includes at least one endpoint of every edge in the graph.
Strongly Connected Component
In a directed graph, a subset of vertices such that there is a directed path from each vertex in the subset to every other vertex.
Incidence Matrix
A matrix that shows the relationship between vertices and edges in a graph.
Edge
A connection between two vertices in a graph.
Connected Graph
A graph where there is a path between every pair of vertices.
Graph Isomorphism
Two graphs G1 and G2 are isomorphic if there is a bijection between their vertex sets that preserves adjacency.
Independent Set
A set of vertices in a graph, no two of which are adjacent.
Degree of a vertex
The number of edges incident to the vertex.
Complete Graph
A graph in which every pair of vertices is connected by an edge.
Degree Sequence
A list of degrees of the vertices in the graph, usually written in non-increasing order.
Eulerian Path
A path in a graph which visits every edge exactly once.
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