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  2. Vertex (graph theory) - Wikipedia

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

    A graph with 6 vertices and 7 edges where the vertex number 6 on the far-left is a leaf vertex or a pendant vertex. In discrete mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph ...

  3. Glossary of graph theory - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_graph_theory

    A one-vertex cut is called an articulation point or cut vertex. vertex set The set of vertices of a given graph G, sometimes denoted by V(G). vertices See vertex. Vizing 1. Vadim G. Vizing 2. Vizing's theorem that the chromatic index is at most one more than the maximum degree. 3.

  4. k-vertex-connected graph - Wikipedia

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

    The vertex-connectivity of an input graph G can be computed in polynomial time in the following way [4] consider all possible pairs (,) of nonadjacent nodes to disconnect, using Menger's theorem to justify that the minimal-size separator for (,) is the number of pairwise vertex-independent paths between them, encode the input by doubling each vertex as an edge to reduce to a computation of the ...

  5. Quadratic function - Wikipedia

    en.wikipedia.org/wiki/Quadratic_function

    To convert the standard form to factored form, one needs only the quadratic formula to determine the two roots r 1 and r 2. To convert the standard form to vertex form, one needs a process called completing the square. To convert the factored form (or vertex form) to standard form, one needs to multiply, expand and/or distribute the factors.

  6. Y-intercept - Wikipedia

    en.wikipedia.org/wiki/Y-intercept

    The -intercept of () is indicated by the red dot at (=, =). In analytic geometry , using the common convention that the horizontal axis represents a variable x {\displaystyle x} and the vertical axis represents a variable y {\displaystyle y} , a y {\displaystyle y} -intercept or vertical intercept is a point where the graph of a function or ...

  7. Independent set (graph theory) - Wikipedia

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

    A vertex coloring of a graph corresponds to a partition of its vertex set into independent subsets. Hence the minimal number of colors needed in a vertex coloring, the chromatic number χ ( G ) {\displaystyle \chi (G)} , is at least the quotient of the number of vertices in G {\displaystyle G} and the independent number α ( G ) {\displaystyle ...

  8. Edge and vertex spaces - Wikipedia

    en.wikipedia.org/wiki/Edge_and_vertex_spaces

    The vertex space of G is the vector space over the finite field of two elements /:= {,} of all functions /. Every element of V ( G ) {\displaystyle {\mathcal {V}}(G)} naturally corresponds the subset of V which assigns a 1 to its vertices.

  9. Complete bipartite graph - Wikipedia

    en.wikipedia.org/wiki/Complete_bipartite_graph

    Regular complex polygons of the form 2{4}p have complete bipartite graphs with 2p vertices (red and blue) and p 2 2-edges. They also can also be drawn as p edge-colorings. Given a bipartite graph, testing whether it contains a complete bipartite subgraph K i , i for a parameter i is an NP-complete problem.