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  2. Vertex cover - Wikipedia

    en.wikipedia.org/wiki/Vertex_cover

    Example graph that has a vertex cover comprising 2 vertices (bottom), but none with fewer. In graph theory, a vertex cover (sometimes node cover) of a graph is a set of vertices that includes at least one endpoint of every edge of the graph. In computer science, the problem of finding a minimum vertex cover is a classical optimization problem.

  3. Clique problem - Wikipedia

    en.wikipedia.org/wiki/Clique_problem

    The brute force algorithm finds a 4-clique in this 7-vertex graph (the complement of the 7-vertex path graph) by systematically checking all C(7,4) = 35 4-vertex subgraphs for completeness. In computer science , the clique problem is the computational problem of finding cliques (subsets of vertices, all adjacent to each other, also called ...

  4. Dijkstra's algorithm - Wikipedia

    en.wikipedia.org/wiki/Dijkstra's_algorithm

    Dijkstra's algorithm (/ ˈ d aɪ k s t r ə z / DYKE-strəz) is an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent, for example, a road network. It was conceived by computer scientist Edsger W. Dijkstra in 1956 and published three years later. [4] [5] [6]

  5. Graph center - Wikipedia

    en.wikipedia.org/wiki/Graph_center

    This is also known as the vertex 1-center problem and can be extended to the vertex k-center problem. Finding the center of a graph is useful in facility location problems where the goal is to minimize the worst-case distance to the facility. For example, placing a hospital at a central point reduces the longest distance the ambulance has to ...

  6. List of NP-complete problems - Wikipedia

    en.wikipedia.org/wiki/List_of_NP-complete_problems

    Partition into cliques is the same problem as coloring the complement of the given graph. A related problem is to find a partition that is optimal terms of the number of edges between parts. [3]: GT11, GT12, GT13, GT14, GT15, GT16, ND14 Grundy number of a directed graph. [3]: GT56 Hamiltonian completion [3]: GT34

  7. Shortest path problem - Wikipedia

    en.wikipedia.org/wiki/Shortest_path_problem

    Shortest path (A, C, E, D, F), blue, between vertices A and F in the weighted directed graph. 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.

  8. Clique (graph theory) - Wikipedia

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

    A simplex graph is an undirected graph κ(G) with a vertex for every clique in a graph G and an edge connecting two cliques that differ by a single vertex. It is an example of median graph, and is associated with a median algebra on the cliques of a graph: the median m(A,B,C) of three cliques A, B, and C is the clique whose vertices belong to ...

  9. Hamiltonian path problem - Wikipedia

    en.wikipedia.org/wiki/Hamiltonian_path_problem

    The problems of finding a Hamiltonian path and a Hamiltonian cycle can be related as follows: In one direction, the Hamiltonian path problem for graph G can be related to the Hamiltonian cycle problem in a graph H obtained from G by adding a new universal vertex x, connecting x to all vertices of G. Thus, finding a Hamiltonian path cannot be ...