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  2. Null graph - Wikipedia

    en.wikipedia.org/wiki/Null_graph

    For each natural number n, the edgeless graph (or empty graph) K n of order n is the graph with n vertices and zero edges. An edgeless graph is occasionally referred to as a null graph in contexts where the order-zero graph is not permitted. [1] [2] It is a 0-regular graph.

  3. Graph (discrete mathematics) - Wikipedia

    en.wikipedia.org/wiki/Graph_(discrete_mathematics)

    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).

  4. Glossary of graph theory - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_graph_theory

    A cut is a partition of the vertices of a graph into two subsets, or the set (also known as a cut-set) of edges that span such a partition, if that set is non-empty. An edge is said to span the partition if it has endpoints in both subsets. Thus, the removal of a cut-set from a connected graph disconnects it. cut point See articulation point ...

  5. Graph coloring - Wikipedia

    en.wikipedia.org/wiki/Graph_coloring

    A graph has a k-coloring if and only if it has an acyclic orientation for which the longest path has length at most k; this is the Gallai–Hasse–Roy–Vitaver theorem (NešetÅ™il & Ossona de Mendez 2012). For planar graphs, vertex colorings are essentially dual to nowhere-zero flows. About infinite graphs, much less is known.

  6. Complete graph - Wikipedia

    en.wikipedia.org/wiki/Complete_graph

    The complement graph of a complete graph is an empty graph. If the edges of a complete graph are each given an orientation, the resulting directed graph is called a tournament. K n can be decomposed into n trees T i such that T i has i vertices. [6] Ringel's conjecture asks if the complete graph K 2n+1 can be decomposed into copies of any tree ...

  7. Isolated point - Wikipedia

    en.wikipedia.org/wiki/Isolated_point

    A closed set with no isolated point is called a perfect set (it contains all its limit points and no isolated points). The number of isolated points is a topological invariant, i.e. if two topological spaces X, Y are homeomorphic, the number of isolated points in each is equal.

  8. Excluded point topology - Wikipedia

    en.wikipedia.org/wiki/Excluded_point_topology

    In mathematics, the excluded point topology is a topology where exclusion of a particular point defines openness. Formally, let X be any non-empty set and p ∈ X. The collection = {:} {} of subsets of X is then the excluded point topology on X. There are a variety of cases which are individually named:

  9. 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 ...