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  2. Graph labeling - Wikipedia

    en.wikipedia.org/wiki/Graph_labeling

    Harmonious labeling. A "harmonious labeling" on a graph G is an injection from the vertices of G to the group of integers modulo k, where k is the number of edges of G, that induces a bijection between the edges of G and the numbers modulo k by taking the edge label for an edge (x, y) to be the sum of the labels of the two vertices x, y (mod k ...

  3. Graph coloring - Wikipedia

    en.wikipedia.org/wiki/Graph_coloring

    Graph coloring. A proper vertex coloring of the Petersen graph with 3 colors, the minimum number possible. In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the ...

  4. Graceful labeling - Wikipedia

    en.wikipedia.org/wiki/Graceful_labeling

    A graceful labeling. Vertex labels are in black, edge labels in red.. In graph theory, a graceful labeling of a graph with m edges is a labeling of its vertices with some subset of the integers from 0 to m inclusive, such that no two vertices share a label, and each edge is uniquely identified by the absolute difference between its endpoints, such that this magnitude lies between 1 and m ...

  5. List of graph theory topics - Wikipedia

    en.wikipedia.org/wiki/List_of_graph_theory_topics

    Total graph. Tree (graph theory). Trellis (graph) Turán graph. Ultrahomogeneous graph. Vertex-transitive graph. Visibility graph. Museum guard problem. Wheel graph.

  6. Tree (graph theory) - Wikipedia

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

    v − 1. Chromatic number. 2 if v > 1. Table of graphs and parameters. 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 ...

  7. Graph canonization - Wikipedia

    en.wikipedia.org/wiki/Graph_canonization

    In graph theory, a branch of mathematics, graph canonization is the problem of finding a canonical form of a given graph G. A canonical form is a labeled graph Canon ( G) that is isomorphic to G, such that every graph that is isomorphic to G has the same canonical form as G. Thus, from a solution to the graph canonization problem, one could ...

  8. Glossary of graph theory - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_graph_theory

    A labeled graph is a graph whose vertices or edges have labels. The terms vertex-labeled or edge-labeled may be used to specify which objects of a graph have labels. Graph labeling refers to several different problems of assigning labels to graphs subject to certain constraints. See also graph coloring, in which the labels are interpreted as ...

  9. Component (graph theory) - Wikipedia

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

    Component (graph theory) In graph theory, a component of an undirected graph is a connected subgraph that is not part of any larger connected subgraph. The components of any graph partition its vertices into disjoint sets, and are the induced subgraphs of those sets. A graph that is itself connected has exactly one component, consisting of the ...

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