Slime moldSlime mold or slime mould is an informal name given to several kinds of unrelated eukaryotic organisms with a life cycle that includes a free-living single-celled stage and the formation of spores. Spores are often produced in macroscopic multicellular or multinucleate fruiting bodies which may be formed through aggregation or fusion. Slime molds were formerly classified as fungi but are no longer considered part of that kingdom. Although not forming a single monophyletic clade, they are grouped within the paraphyletic group Protista.
List of graphsThis partial list of graphs contains definitions of graphs and graph families. For collected definitions of graph theory terms that do not refer to individual graph types, such as vertex and path, see Glossary of graph theory. For links to existing articles about particular kinds of graphs, see . Some of the finite structures considered in graph theory have names, sometimes inspired by the graph's topology, and sometimes after their discoverer.
Line graphIn the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges of G. L(G) is constructed in the following way: for each edge in G, make a vertex in L(G); for every two edges in G that have a vertex in common, make an edge between their corresponding vertices in L(G). The name line graph comes from a paper by although both and used the construction before this.
Planar graphIn graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other. Such a drawing is called a plane graph or planar embedding of the graph. A plane graph can be defined as a planar graph with a mapping from every node to a point on a plane, and from every edge to a plane curve on that plane, such that the extreme points of each curve are the points mapped from its end nodes, and all curves are disjoint except on their extreme points.
Chordal graphIn the mathematical area of graph theory, a chordal graph is one in which all cycles of four or more vertices have a chord, which is an edge that is not part of the cycle but connects two vertices of the cycle. Equivalently, every induced cycle in the graph should have exactly three vertices. The chordal graphs may also be characterized as the graphs that have perfect elimination orderings, as the graphs in which each minimal separator is a clique, and as the intersection graphs of subtrees of a tree.
Graph isomorphismIn 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 being a structure-preserving bijection. If an isomorphism exists between two graphs, then the graphs are called isomorphic and denoted as . In the case when the bijection is a mapping of a graph onto itself, i.
Dense graphIn mathematics, a dense graph is a graph in which the number of edges is close to the maximal number of edges (where every pair of vertices is connected by one edge). The opposite, a graph with only a few edges, is a sparse graph. The distinction of what constitutes a dense or sparse graph is ill-defined, and is often represented by 'roughly equal to' statements. Due to this, the way that density is defined often depends on the context of the problem.
Petersen graphIn the mathematical field of graph theory, the Petersen graph is an undirected graph with 10 vertices and 15 edges. It is a small graph that serves as a useful example and counterexample for many problems in graph theory. The Petersen graph is named after Julius Petersen, who in 1898 constructed it to be the smallest bridgeless cubic graph with no three-edge-coloring. Although the graph is generally credited to Petersen, it had in fact first appeared 12 years earlier, in a paper by .
Urban sprawlUrban sprawl (also known as suburban sprawl or urban encroachment) is defined as "the spreading of urban developments (such as houses and shopping centers) on undeveloped land near a city". Urban sprawl has been described as the unrestricted growth in many urban areas of housing, commercial development, and roads over large expanses of land, with little concern for urban planning. In addition to describing a special form of urbanization, the term also relates to the social and environmental consequences associated with this development.
Graph operationsIn the mathematical field of graph theory, graph operations are operations which produce new graphs from initial ones. They include both unary (one input) and binary (two input) operations. Unary operations create a new graph from a single initial graph. Elementary operations or editing operations, which are also known as graph edit operations, create a new graph from one initial one by a simple local change, such as addition or deletion of a vertex or of an edge, merging and splitting of vertices, edge contraction, etc.
Bipartite graphIn the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets and , that is, every edge connects a vertex in to one in . Vertex sets and are usually called the parts of the graph. Equivalently, a bipartite graph is a graph that does not contain any odd-length cycles. The two sets and may be thought of as a coloring of the graph with two colors: if one colors all nodes in blue, and all nodes in red, each edge has endpoints of differing colors, as is required in the graph coloring problem.
ProtistA protist (ˈproʊtᵻst ) or protoctist is any eukaryotic organism that is not an animal, plant, or fungus. Protists do not form a natural group, or clade, but an artificial grouping of several independent clades that evolved from the last eukaryotic common ancestor. Protists were historically regarded as a separate taxonomic kingdom known as Protista or Protoctista. With the advent of phylogenetic analysis and electron microscopy studies, the use of Protista as a formal taxon was gradually abandoned.
Physarum polycephalumPhysarum polycephalum, an acellular slime mold or myxomycete popularly known as "the blob", is a protist with diverse cellular forms and broad geographic distribution. The “acellular” moniker derives from the plasmodial stage of the life cycle: the plasmodium is a bright yellow macroscopic multinucleate coenocyte shaped in a network of interlaced tubes. This stage of the life cycle, along with its preference for damp shady habitats, likely contributed to the original mischaracterization of the organism as a fungus.
Urban decayUrban decay (also known as urban rot, urban death or urban blight) is the sociological process by which a previously functioning city, or part of a city, falls into disrepair and decrepitude. There is no single process that leads to urban decay. Urban decay can include the following aspects: Industrialization Deindustrialization Gentrification Population decline or overpopulation Counterurbanization Economic Restructuring Multiculturalism Abandoned buildings or infrastructure High local unemployment Increased poverty Fragmented families Low overall living standards or quality of life Political disenfranchisement Crime (e.
MyxogastriaMyxogastria/Myxogastrea (myxogastrids, ICZN) or Myxomycetes (ICN), is a class of slime molds that contains 5 orders, 14 families, 62 genera, and 888 species. They are colloquially known as the plasmodial or acellular slime moulds. All species pass through several, very different morphologic phases, such as microscopic individual cells, slimy amorphous organisms visible with the naked eye and conspicuously shaped fruit bodies. Although they are monocellular, they can reach immense widths and weights: in extreme cases they can be up to across and weigh up to .
Graph theoryIn 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 links or lines). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics.
Signed graphIn the area of graph theory in mathematics, a signed graph is a graph in which each edge has a positive or negative sign. A signed graph is balanced if the product of edge signs around every cycle is positive. The name "signed graph" and the notion of balance appeared first in a mathematical paper of Frank Harary in 1953. Dénes Kőnig had already studied equivalent notions in 1936 under a different terminology but without recognizing the relevance of the sign group.
Urban areaAn urban area, built-up area or urban agglomeration is a human settlement with a high population-density and an infrastructure of built environment. This is the core of a metropolitan statistical area in the United States, if it contains a population of more than 50,000. Urban areas originate through urbanization, and researchers categorize them as cities, towns, conurbations or suburbs. In urbanism, the term "urban area" contrasts to rural areas such as villages and hamlets; in urban sociology or urban anthropology it contrasts with natural environment.
Shortest path problemIn 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, where the vertices correspond to intersections and the edges correspond to road segments, each weighted by the length of the segment.
Outerplanar graphIn graph theory, an outerplanar graph is a graph that has a planar drawing for which all vertices belong to the outer face of the drawing. Outerplanar graphs may be characterized (analogously to Wagner's theorem for planar graphs) by the two forbidden minors K4 and K2,3, or by their Colin de Verdière graph invariants. They have Hamiltonian cycles if and only if they are biconnected, in which case the outer face forms the unique Hamiltonian cycle. Every outerplanar graph is 3-colorable, and has degeneracy and treewidth at most 2.
