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  2. Seven Bridges of Königsberg - Wikipedia

    en.wikipedia.org/wiki/Seven_Bridges_of_Königsberg

    The resulting mathematical structure is a graph. → → Since only the connection information is relevant, the shape of pictorial representations of a graph may be distorted in any way, without changing the graph itself. Only the number of edges (possibly zero) between each pair of nodes is significant.

  3. Graph theory - Wikipedia

    en.wikipedia.org/wiki/Graph_theory

    A drawing of a graph. In mathematics, 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 ).

  4. Shortest path problem - Wikipedia

    en.wikipedia.org/wiki/Shortest_path_problem

    In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized. The problem of finding the shortest path between two intersections on a road map may be modeled as a special case of the shortest path problem in graphs ...

  5. List of NP-complete problems - Wikipedia

    en.wikipedia.org/wiki/List_of_NP-complete_problems

    NP-complete special cases include the edge dominating set problem, i.e., the dominating set problem in line graphs. NP-complete variants include the connected dominating set problem and the maximum leaf spanning tree problem. [ 3]: ND2. Feedback vertex set [ 2][ 3]: GT7. Feedback arc set [ 2][ 3]: GT8.

  6. Blossom algorithm - Wikipedia

    en.wikipedia.org/wiki/Blossom_algorithm

    In graph theory, the blossom algorithm is an algorithm for constructing maximum matchings on graphs. The algorithm was developed by Jack Edmonds in 1961, [1] and published in 1965. [2] Given a general graph G = (V, E), the algorithm finds a matching M such that each vertex in V is incident with at most one edge in M and |M| is maximized.

  7. NP-completeness - Wikipedia

    en.wikipedia.org/wiki/NP-completeness

    An interesting example is the graph isomorphism problem, the graph theory problem of determining whether a graph isomorphism exists between two graphs. Two graphs are isomorphic if one can be transformed into the other simply by renaming vertices. Consider these two problems: Graph Isomorphism: Is graph G 1 isomorphic to graph G 2?

  8. Graph isomorphism - Wikipedia

    en.wikipedia.org/wiki/Graph_isomorphism

    Graph isomorphism. In graph theory, an isomorphism of graphs G and H is a bijection between the vertex sets of G and H. such that any two vertices u and v of G are adjacent in G if and only if and are adjacent in H. This kind of bijection is commonly described as "edge-preserving bijection", in accordance with the general notion of isomorphism ...

  9. Algebraic graph theory - Wikipedia

    en.wikipedia.org/wiki/Algebraic_graph_theory

    Algebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs. This is in contrast to geometric, combinatoric, or algorithmic approaches. There are three main branches of algebraic graph theory, involving the use of linear algebra, the use of group theory, and the study of graph invariants .