Graph families als Taschenbuch von - Paperback

Source: Wikipedia. Pages: 84. Chapters: Planar graph, Regular graph, Expander graph, Extractor, Disperser, Median graph, Apollonian network, Pseudoforest, Claw-free graph, Scale-free network, Hypohamiltonian graph, Apex graph, Small-world network, Distance-hereditary graph, Line graph, Outerplanar graph, Skew-symmetric graph, Cayley graph, Triangle-free graph, Forbidden graph characterization, Split graph, Chordal graph, Cubic graph, Comparability graph, Gallery of named graphs, Snark, Biased graph, Cograph, Line graph of a hypergraph, Moore graph, Series-parallel graph, Partial cube, Trivially perfect graph, Bipartite graph, Cactus graph, Block graph, Distance-transitive graph, Strongly chordal graph, Simplex graph, Distance-regular graph, Universal graph, Strongly regular graph, Halin graph, Threshold graph, Toroidal graph, Cage, Generalized scale-free model, Aperiodic graph, Squaregraph, Vertex-transitive graph, Ramanujan graph, Dense graph, Asymmetric graph, K-Variegated graph, Quasi-bipartite graph, Even-hole-free graph, Critical graph, K-tree, Semi-symmetric graph, List of graphs, Convex bipartite graph, Laman graph, K-vertex-connected graph, Biconnected graph, Self-complementary graph, K-edge-connected graph, Half-transitive graph, Lévy family of graphs, Edge-transitive graph, Lattice graph, Implication graph, Overfull graph, Bound graph, Reeb graph, Conference graph, Integral graph, Hanan grid, Factor-critical graph, Quartic graph, Trellis. Excerpt: In mathematics, and more specifically graph theory, a median graph is an undirected graph in which any three vertices a, b, and c have a unique median: a vertex m(a,b,c) that belongs to shortest paths between any two of a, b, and c. The concept of median graphs has long been studied, for instance by Birkhoff & Kiss (1947) or (more explicitly) by Avann (1961), but the first paper to call them "median graphs" appears to be Nebesk'y (1971). As Chung, Graham, and Saks write, "median graphs arise naturally in the study of ordered sets and discrete distributive lattices, and have an extensive literature". In phylogenetics, the Buneman graph representing all maximum parsimony evolutionary trees is a median graph. Median graphs also arise in social choice theory: if a set of alternatives has the structure of a median graph, it is possible to derive in an unambiguous way a majority preference among them. Additional surveys of median graphs are given by Klavzar & Mulder (1999), Bandelt & Chepoi (2008), and Knuth (2008). The median of three vertices in a tree, showing the subtree formed by the union of shortest paths between the vertices.Any tree is a median graph. To see this, observe that in a tree, the union of the three shortest paths between any three vertices a, b, and c is either itself a path, or a subtree formed by three paths meeting at a single central node with degree three. If the union of the three paths is itself a path, the median m(a,b,c) is equal to one of a, b, or c, whichever of these three vertices is between the other two in the path. If the subtree formed by the union of the three paths is not a path, the median of the three vertices is the central degree-three node of the subtree. Additional examples of median graphs are provided by the grid graphs. In a grid graph, the coordinates of the median m(a,b,c) can be found as the median of the coordinates of a, b, and c. Conversely, it turns out that, in any median graph, one may label the vertices by points