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2. Connectivity (graph theory) - Wikipedia

   en.wikipedia.org/wiki/Connectivity_(graph_theory)

   This graph becomes disconnected when the right-most node in the gray area on the left is removed This graph becomes disconnected when the dashed edge is removed.. In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more ...

3. k-vertex-connected graph - Wikipedia

   en.wikipedia.org/wiki/K-vertex-connected_graph

   A graph with connectivity 4. In graph theory, a connected graph G is said to be k-vertex-connected (or k-connected) if it has more than k vertices and remains connected whenever fewer than k vertices are removed. The vertex-connectivity, or just connectivity, of a graph is the largest k for which the graph is k-vertex-connected.

4. Strongly connected component - Wikipedia

   en.wikipedia.org/wiki/Strongly_connected_component

   The strongly connected components of a directed graph form a partition into subgraphs that are themselves strongly connected. It is possible to test the strong connectivity of a graph, or to find its strongly connected components, in linear time (that is, Θ( V + E )).

5. Tree (graph theory) - Wikipedia

   en.wikipedia.org/wiki/Tree_(graph_theory)

   In graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected acyclic undirected graph. [1] A forest is an undirected graph in which any two vertices are connected by at most one path, or equivalently an acyclic undirected graph, or equivalently a disjoint union of trees.

6. Component (graph theory) - Wikipedia

   en.wikipedia.org/wiki/Component_(graph_theory)

   Additional examples include the following special cases: In an empty graph, each vertex forms a component with one vertex and zero edges. [3] More generally, a component of this type is formed for every isolated vertex in any graph. [4] In a connected graph, there is exactly one component: the whole graph. [4] In a forest, every component is a ...

7. Graph theory - Wikipedia

   en.wikipedia.org/wiki/Graph_theory

   In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points ) which are connected by edges (also called arcs , links or lines ).

8. k-edge-connected graph - Wikipedia

   en.wikipedia.org/wiki/K-edge-connected_graph

   In graph theory, a connected graph is k-edge-connected if it remains connected whenever fewer than k edges are removed. The edge-connectivity of a graph is the largest k for which the graph is k-edge-connected. Edge connectivity and the enumeration of k-edge-connected graphs was studied by Camille Jordan in 1869. [1]

9. List of graph theory topics - Wikipedia

   en.wikipedia.org/wiki/List_of_graph_theory_topics

   1 Examples and types of graphs. 2 Graph coloring. 3 Paths and cycles. ... This is a list of graph theory topics, ... Strongly connected component;