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The number of edges incident to the vertex.

A set of vertices connected by edges.

A connection between two vertices in a graph.

A sequence of vertices where each adjacent pair is connected by an edge.

A path that starts and ends at the same vertex without traversing any other vertex more than once.

A graph where there is a path between every pair of vertices.

A graph formed from a subset of the vertices and edges of another graph.

A graph in which every pair of vertices is connected by an edge.

A connected graph with no cycles.

A collection of trees.

A graph whose vertices can be divided into two disjoint sets such that no two vertices within the same set are adjacent.

A graph in which the edges have a direction.

A graph where edges have an associated weight or cost.

A graph that can be embedded in the plane, so no edges intersect except at their endpoints.

Two vertices are adjacent if they are connected by an edge.

A list of degrees of the vertices in the graph, usually written in non-increasing order.

A path in a graph which visits every edge exactly once.

A path in a graph that visits each vertex exactly once.

Two graphs G1 and G2 are isomorphic if there is a bijection between their vertex sets that preserves adjacency.

A set of vertices that includes at least one endpoint of every edge in the graph.

A set of vertices in a graph, no two of which are adjacent.

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.

A square matrix used to represent a finite graph, with rows and columns labeled by graph vertices.

A matrix that shows the relationship between vertices and edges in a graph.