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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 ...
Build n copies of the star graph on 4 vertices. Denote the central vertex of each star A i and the outer vertices B i, C i and D i. This results in a disconnected graph on 4n vertices with 3n edges (A i – B i, A i – C i and A i – D i for 1 ≤ i ≤ n). Construct the n-cycle (B 1... B n). This adds n edges. Finally construct the 2n-cycle ...
The remaining sub-graph (g) produced by the algorithm is not disconnected since the algorithm checks for that in line 7. The result sub-graph cannot contain a cycle since if it does then when moving along the edges we would encounter the max edge in the cycle and we would delete that edge. Thus g must be a spanning tree of the main graph G.
The graph on the upper left can be strongly oriented, as shown by the lower left graph which is strongly connected. The lower right is an orientation of the upper right graph, but not a strong one. In graph theory , a strong orientation of an undirected graph is an assignment of a direction to each edge (an orientation ) that makes it into a ...
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.
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 ).
A graph with three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs {,} of vertices, whose elements are called edges (sometimes links or lines).
This is a list of graph theory topics, by Wikipedia page. See glossary of graph theory for basic terminology. Examples and types of graphs. Amalgamation;