In graph theory, a division of mathematics, a median graph is an undirected graph in which every three vertices a, b, and c have a unique median: a vertex m(a,b,c) that belongs to shortest paths between each pair 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 Nebeský (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".[1] In phylogenetics, the Buneman graph representing all maximum parsimony evolutionary trees is a median graph.[2] 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.[3]
Additional surveys of median graphs are given by Klavžar & Mulder (1999), Bandelt & Chepoi (2008), and Knuth (2008).
In graph theory, a division of mathematics, a mediangraph is an undirected graph in which every three vertices a, b, and c have a unique median: a vertex...
of mediangraphs, and every mediangraph is a partial cube. Bipartite graphs may be characterized in several different ways: An undirected graph is bipartite...
descriptions of redirect targets Mediangraph – Graph with a median for each three vertices Median of medians – Fast approximate median algorithm – Algorithm to...
Appendix:Glossary of graph theory in Wiktionary, the free dictionary. This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes...
In graph theory, a lattice graph, mesh graph, or grid graph is a graph whose drawing, embedded in some Euclidean space R n {\displaystyle \mathbb {R}...
In graph theory, the hypercube graph Qn is the graph formed from the vertices and edges of an n-dimensional hypercube. For instance, the cube graph Q3...
two hypercube graphs is another hypercube: Qi□Qj = Qi+j. The Cartesian product of two mediangraphs is another mediangraph. The graph of vertices and...
complement graph of a path graph is a Fibonacci cube. The complete subgraphs of G can be given the structure of a median algebra: the median of three cliques...
In graph theory, a branch of mathematics, the modular graphs are undirected graphs in which every three vertices x, y, and z have at least one median vertex...
point set to reduce the cost of connecting the points The median of three vertices in a mediangraph, the solution to the Steiner tree problem for those three...
In the mathematical field of graph theory, a complete bipartite graph or biclique is a special kind of bipartite graph where every vertex of the first...
In graph theory, a perfect graph is a graph in which the chromatic number equals the size of the maximum clique, both in the graph itself and in every...
In the mathematical field of graph theory, a graph homomorphism is a mapping between two graphs that respects their structure. More concretely, it is a...
classes of graphs including mediangraphs have related definitions involving metric embeddings (Bandelt & Chepoi 2008). A flip graph is a graph formed from...
then this graph is a mediangraph, and it accurately represents the algebra in that the median operation defined by shortest paths on the graph coincides...
In graph theory, a branch of combinatorial mathematics, a block graph or clique tree is a type of undirected graph in which every biconnected component...
subjects survive 3.72 months. Median survival is thus 3.72 months. In some cases, median survival cannot be determined from the graph. For example, for survival...
elements. If a lattice is distributive, its covering relation forms a mediangraph. Furthermore, every distributive lattice is also modular. The introduction...
Desargues graph. All mediangraphs are partial cubes. The trees and hypercube graphs are examples of mediangraphs. Since the mediangraphs include the squaregraphs...
Therefore, like other simplex graphs, Fibonacci cubes are mediangraphs and more generally partial cubes. The median of any three vertices in a Fibonacci...
the median of the three doctors matched to it. More generally, any set of an odd number of elements of any distributive lattice (or mediangraph) has...
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