adj
(graph theory, of a graph) Containing no cycles.
n
(graph theory, computer science) A directed acyclic graph, a finite directed graph that contains no directed cycles.
n
(mathematics) A collection of unordered lists (each representing the neighbours of a vertex) that represents a finite graph
n
(graph theory) A matrix showing which vertices of a graph are adjacent to which other vertices.
n
(graph theory) The maximum number of edge-disjoint cyclic subgraphs of a graph G whose union is G.
n
(graph theory) A cycle in the complement of a given graph.
adj
(graph theory) Having arcs that alternate between forward and backward arcs.
n
(graph theory) A directed rooted tree in which all vertices can be reached from the root.
n
(graph theory) The minimum number of forests into which the edges of an undirected graph may be partitioned.
n
(graph theory) A directed edge.
n
(graph theory) A directed edge.
n
(graph theory, computing) An algorithm that computes single-source shortest paths in a weighted digraph, capable (unlike the faster Dijkstra's algorithm) of handling graphs with negative edge weights.
n
(graph theory) A kind of connected cycle-free graph.
n
(graph theory, countable) A measure of the number of geodesic paths through a node or edge.
adj
(graph theory) Describing a connected graph from which two vertices must be removed for it to become disconnected.
adj
(mathematics) Describing a graph, each of whose edge has an independent orientation at each end
n
(mathematics) A binary tree.
n
A greedy algorithm for finding a minimum spanning tree in a graph, or a minimum spanning forest in the case of a graph that is not connected.
n
(graph theory) The length of the longest path between two vertices in a graph.
n
(graph theory) A search algorithm that begins at the root node and explores all the neighboring nodes.
n
(graph theory) An edge which, if removed, changes a connected graph to one that is not connected.
n
(graph theory) A regular graph that has as few vertices as possible for its girth.
n
(algebra) the underlying set of an algebraic structure
n
(mathematics) A set of subtrees of a tree
n
(graph theory) A tree consisting of only a path (the spine or stalk of the tree) and vertices directly connected to (i.e. one edge away from) that path; a tree whose vertices with a degree of at least 3 are all surrounded by at most two vertices of degree two or greater.
n
A graph (collection of vertices and edges) encoding information about a group and its generators.
n
(graph theory) A formula for the number of spanning trees of a complete graph of n vertices: nⁿ⁻².
n
(graph theory, of a tree) Given a tree of n nodes, either (1) a unique node whose removal would split the tree into subtrees of fewer than n/2 nodes, or (2) either of a pair of adjacent nodes such that removal of the edge connecting them would split the tree into two subtrees of exactly n/2 nodes.
n
(countable, mathematics) A complex number representing an element of a finite Abelian group.
n
(graph theory) The problem of finding the shortest closed path or circuit that visits every edge of a (connected) undirected graph.
n
(graph theory) An edge that is not part of a cycle but connects two vertices of the cycle.
adj
(graph theory) For a graph, in which all cycles of four or more vertices have a chord.
adj
(graph theory) Lacking chords.
n
(mathematics) The number of independent cycles in a graph
n
(graph theory) The length of the longest cycle of a graph
n
(graph theory) The number of vertices in a maximum clique of a given graph.
adj
(graph theory, of a walk) Whose first and last vertices are the same, forming a closed loop.
n
(mathematics) The smallest set that both includes a given subset and possesses some given property.
n
(mathematics) A graph consisting of two rows of paired nodes in which all nodes except the paired ones are connected with straight lines; it is the complement of the ladder graph, and the dual graph of the hypercube.
n
(graph theory) a subgraph whose complement is a clique, i.e. an independent set
n
(mathematics) The number of edges of a hypergraph that contain all the specified vertices
n
(mathematics) A graph formed from another by complementation and disjoin union.
n
(graph theory) A node in a causal graph that has at least two incoming edges.
n
(graph theory) An assignment of a color to each vertex of a graph such that no two vertices connected by an edge are given the same color.
n
(graph theory) A directed acyclic combined graph.
adj
(mathematics) Pertaining to an associated simple root that occurs with coefficient 1 in the highest root of a subgroup.
n
(graph theory) A biclique, a bipartite graph such that every vertex of one set is connected to every vertex of the other.
n
(graph theory) A graph where every pair of vertices is connected by an edge.
adj
(mathematics, graph theory, of a graph) Having a path, either directed or undirected, connecting every pair of vertices.
n
(mathematics) A graph in which there is a route of edges and nodes connecting any two nodes.
adj
(mathematics) Having a null complement
n
(mathematics) The structure produced by the intersection of multiple related curves or shapes.
n
(graph theory) The number of vertices in a minimum vertex cover of a graph, often denoted as 𝜏=𝜏(G).
n
(graph theory) An undirected graph with 2n vertices in the two sets { u₁, u₂, ..., uₙ } and { v₁, v₂, ..., vₙ } and with an edge from uᵢ to vⱼ whenever i ≠ j.
n
(mathematics) The set of edges (of a cut) whose endpoints are in different subsets of the partition
n
(graph theory) The minimum number of edges that cross any cut between lower-numbered and higher-numbered vertices in an optimal linear arrangement of the vertices of a graph.
n
(graph theory) A closed walk or path, with or without repeated vertices allowed.
n
(mathematics) A chord of a graph cycle, one of whose endpoints is not a vertex.
adj
(graph theory) Used to describe the number of edges that must be removed from a graph to ensure that no graph cycle remains; equal to the number of edges, minus the number of nodes plus one.
n
(graph theory) A directed acyclic graph; an ordered pair (V,E) such that E is a subset of some partial ordering relation on V.
adj
(mathematics) Describing the smallest number of vertices that can be removed from a graph such that no cycles remain
n
(mathematics) A monotonic nonincreasing sequence of the vertex degrees of the vertices of a graph
n
(graph theory) An algorithm for traversing a tree or graph where one starts at the root and explores as far as possible along each branch before backtracking.
n
(graph theory) A distance-transitive cubic graph with 20 vertices and 30 edges.
n
(graph theory) The maximum eccentricity over all vertices in a graph.
adj
(mathematics, of a graph) Strongly connected
n
(graph theory) directed cycle
n
(mathematics) The girth of a digraph
n
(graph theory) A directed graph.
n
(graph theory) An algorithm that computes single-source shortest paths in a weighted digraph.
n
(graph theory) directed path
adj
(graph theory) Having the properties of a directed graph.
n
(graph theory, computer science) A finite directed graph that contains no directed cycles.
n
(graph theory) An edge of a directed graph.
n
(graph theory) A graph in which the edges are ordered pairs, so that, if the edge (a, b) is in the graph, the edge (b, a) need not be in the graph and is distinct from (a, b) if it is.
n
(graph theory) In a directed graph, a path in which the edges are all oriented in the same direction.
adj
(mathematics) Describing a graph (or network) in which nodes of low degree are more likely to connect with nodes of a high degree
n
(geometry) The invariant (on the vector space of forms of degree d in n variables) that vanishes exactly when the corresponding hypersurface in Pⁿ⁻¹ is singular.
n
(graph theory) A set of vertices of a graph, such that each vertex in that graph is either in that set or adjacent to a vertex in that set.
n
(graph theory) the number of vertices in a minimum dominating set of a given graph, often denoted as 𝛾=𝛾(G)
n
(graph theory) A node that dominates another.
n
(mathematics) A point on a curve at which there are two tangents (because it touches itself, or has a cusp).
n
(graph theory) A graph derived from some plane graph in such a way that the derived graph has a vertex corresponding to each face of the given graph, an edge corresponding to each edge of the given graph that is shared by a pair of distinct faces, and a self-loop for each edge of the given graph that is a border of the same face on both of its sides.
n
(graph theory) A connected pair of vertices in a graph.
n
(graph theory) A set of edges which touch all the vertices of a graph.
n
(graph theory) The number of edges in a minimum edge cover of a graph, often denoted as 𝜌=𝜌(G).
n
(mathematics) An ordered list of the edges of a graph (set of connected vertices)
n
(mathematics) The set of all the edges of a graph
n
(graph theory) A graph with vertices but no edges.
n
(mathematics) Either of the two nodes of a graph of degree 1.
n
(graph theory) An algorithm that finds a number of shortest paths (allowing cycles) connecting a given pair of vertices in a digraph.
adj
(mathematics) Of surds: arising from the extraction of the same nth root.
n
(graph theory) An Eulerian path, a looped path through a graph that passes along every edge exactly once.
n
(graph theory) an Eulerian trail that begins and ends at the same node
n
(graph theory) a trail that visits each node exactly once
n
(graph theory) A particular kind of bipartite graph.
n
(mathematics) A diagram that shows the possible partitions of a positive integer as rows of dots.
n
(computing theory) An iterative heuristic algorithm for bipartitioning a hypergraph.
n
(computer science, graph theory) An algorithm for finding shortest paths in a weighted graph with positive or negative edge weights (but with no negative cycles).
n
(graph theory) The length of the shortest cycle in a graph.
n
(calculus, of a function) The ratio of the rates of change of a dependent variable and an independent variable, the slope of a curve's tangent.
n
(graph theory) A set of vertices (or nodes) connected together by edges; (formally) an ordered pair of sets (V,E), where the elements of V are called vertices or nodes and E is a set of pairs (called edges) of elements of V. See also Graph (discrete mathematics) on Wikipedia.Wikipedia
n
(mathematics) The complement of a graph hole
n
(mathematics) A cycle, in a graph, that has no cycle chord
n
(mathematics) A measure, expressed by a positive integer (with the exception of complete graphs), of the connectivity of a graph.
n
(mathematics) A generalisation of a (possibly disconnected) graphlet
n
(mathematics) A small, connected, non-isomorphic, induced subgraph of a large network
n
(mathematics, graph theory) The completion of the metric space of the set of finite graphs endowed with the cut metric.
n
(graph theory) An edge that is attached to only one node, rather than connecting two of them, or is connected in only one direction
adj
(mathematics, graph theory, of a cycle/path) That visits each vertex exactly once.
n
(graph theory) A Hamiltonian path with an additional connection between the first and last vertices visited, forming a cycle.
n
(graph theory) A graph for which there is a Hamiltonian cycle.
n
(mathematics) The group of instances at the head (high end) of a distribution curve
n
(mathematics, graph theory) A bipartite undirected graph with 11 vertices and 18 edges that is the smallest non-Hamiltonian polyhedral graph.
n
(graph theory) A chordless cycle in a graph.
n
(graph theory) A directed edge in a hypergraph.
n
(graph theory) The equivalent of a graph's edge in a hypergraph.
n
(mathematics) A generalization of a graph, in which edges can connect any number of vertices.
adj
(mathematics) Containing a closed circuit that visits one vertex exactly twice and all other vertices exactly once.
n
(mathematics) interpolation on a surface of more than two dimensions
n
(mathematics) A probabilistic graphical model based on hypergraph models and inspired by biological systems.
n
(graph theory) A kind of graph whose node set can contain other graphs as well as basic nodes.
n
(philosophy) An uncountably infinite number of operations that occur sequentially within a finite interval of time.
n
(mathematics) A form of hypergraph based on trees.
adj
(graph theory) Of a graph, not containing a Hamiltonian cycle but such that the removal of any single vertex produces a Hamiltonian graph.
adj
(graph theory) hypohamiltonian.
n
(mathematics) A function that assigns a pair of vertices to each edge of a graph.
n
(graph theory) The number of edges directed into a vertex in a directed graph
n
(graph theory) the number of vertices in a maximum independent set of a given graph, often denoted as 𝛼=𝛼(G)
n
(graph theory) a set of vertices of a graph, such that no pair of them are adjacent to each other; in other words, a set of vertices which are all "independent" of each other
n
(graph theory) An incoming edge in a digraph, i.e. one that enters a particular node.
n
(graph theory) A set of vertices of a graph after whose deletion the graph is no longer connected.
n
(graph theory) An edge in a graph whose deletion increases the number of connected components of the graph.
n
(graph theory) An algorithm for finding the shortest paths between all pairs of vertices in an edge-weighted directed graph.
n
Used other than figuratively or idiomatically: see Jordan curve, theorem.
n
(graph theory) A vertex in a directed graph which can reach every other vertex via a path with a length of at most 2.
n
(Rubik's Cube) An algorithm for solving the Rubik's Cube, an improvement on Thistlethwaite's algorithm.
n
(Rubik's Cube) An algorithm for solving the Rubik's Cube by iterative deepening.
n
A linear time algorithm to find the strongly connected components of a directed graph.
n
An algorithm in discrete mathematics/graph theory that is used to generate the minumum spanning tree in a given direction of two paths. It translates a forest from the nodes in the graph, considering each node as its own tree.
n
(mathematics) A theorem stating that the set of finite trees over a well-quasi-ordered set of labels is itself well-quasi-ordered under homeomorphic embedding.
n
(mathematics) A bipartite graph associated with an incidence structure.
n
(computing theory) In combinatorial optimization, a heuristic for solving the symmetric travelling salesman problem, involving the swapping of pairs of subtours to make a new tour.
n
(graph theory) An edge of a graph.
n
(graph theory) A graph L(G) which is derived from a given non-oriented graph G such that the vertices of L(G) represent edges of G and so that a clique in L(G) represents a common end-vertex shared by a set of represented edges. (A star subgraph in G transforms into a clique in L(G).)
adj
(mathematics, of a graph) For which every vertex has finite degree.
n
(graph theory) An edge that begins and ends on the same vertex.
n
(graph theory) half-edge
n
(mathematics, chiefly historical) Synonym of pi, particularly the 35-decimal approximation discovered by Ludolph van Ceulen
n
(mathematics) A weighted planar graph having some external nodes
n
(graph theory) A set of independent edges in a given graph, i.e. a set of edges which do not intersect, such that pairs of vertices are "matched" to each other one to one.
n
(graph theory) the number of edges in a maximum matching, often denoted 𝜈=𝜈(G)
n
(graph theory) A characterization of the connectivity in finite undirected graphs in terms of the minimum number of disjoint paths that can be found between any pair of vertices.
n
(graph theory) A cut that is minimal in some metric.
n
A spanning tree that has minimum possible weight for a given graph
n
(graph theory) A regular graph of degree d and diameter k whose number of vertices equals the upper bound 1+d∑ᵢ₌₀ᵏ⁻¹(d-1)ⁱ.
n
(graph theory) A set V (whose elements are called vertices or nodes), taken together with a multiset E, each of whose elements (called an edge or line) is a cardinality-two multisubset of V.
n
(mathematics) An acyclic directed graph in which the set of nodes reachable from any node forms a tree.
n
(graph theory) A vertex or a leaf in a graph of a network, or other element in a data structure.
n
(mathematics) The value of a node of a tree.
n
(mathematics) A subset of vertices in an undirected graph, all of which are adjacent to vertices outside of the subset
adj
(graph theory) Of a digraph, having no cycles of even weight
adj
(graph theory, of a walk) Whose first and last vertices are different.
n
(topology, mathematical analysis, restricted to metric spaces) The set of all points in a metric space whose distance from a given point ("the open ball's center") is less than a given length ("the open ball's radius").
n
(graph theory) The number of vertices in a graph.
n
(graph theory) A theorem that considers the sum of the degrees of pairs of non-adjacent vertices: if every such pair has a sum that at least equals the total number of vertices in the graph, then the graph is Hamiltonian.
n
(graph theory) The number of edges directed out of a vertex in a directed graph.
n
(graph theory) An outgoing edge in a digraph, i.e. one that leaves a particular node.
n
(graph theory) The number of edges traversed in a given path in a graph.
n
(graph theory) A measure of a path decomposition of a graph.
adj
The ordinal form of the number pi.
n
(mathematics) An ordered tree, a type of graph, in which the child nodes of each vertex have a definite number assigned.
n
(computing) A hierarchical relationship (tree) in which at least one child has more than one parent
n
(graph theory) a graph with at most one undirected path between any two vertices. In other words, a directed acyclic graph (DAG) for which there are no undirected cycles either.
adj
(linear algebra) Said of a quadratic form: that the application of it to a tuple is greater or equal to zero, only equaling zero if the tuple itself is zero.
v
(graph theory) A node z postdominates a node n if all paths to the exit node of the graph starting at n must go through z
n
(graph theory) A node that postdominates another.
n
(graph theory) A positive feedback cycle where the more connected nodes in a graph are more likely to receive new links.
n
(number theory, recreational mathematics) A magic square using the decimal digits of the reciprocal of a prime number.
n
(graph theory) A graph that resembles a directed graph but violates one of the normal rules, as for example by including a directed loop.
n
(graph theory) an undirected graph in which every connected component has at most one cycle
n
(graph theory) A graph that contains loops as well as multiple edges between vertices
n
(mathematics) The size of any basis of a given matroid.
adj
(mathematics) (of a node) That may be reached from another node in a graph by passing along one or more lines
n
(graph theory) A triangle-free connected graph where any two vertices have 0 or 2 common neighbors.
n
(mathematics) A composite number; or a composite number which is not a square; or a composite number which is neither square nor heteromecic.
n
(graph theory) A graph whose vertices all have the same degree.
n
(graph theory, computing) The single node of a tree that has no parent.
n
(mathematics) The vector space generated by all the row vectors of a matrix.
n
(graph theory) A cut that requires the source and the sink to be in different subsets, and its cut-set only consisting of edges going from the source's side to the sink's side.
adj
(mathematics, graph theory) of or pertaining to a graph in which, for any two verticies u, v in the graph, there is another vertex w which is adjacent to both u and v (i.e. u,w,v is a path in that graph).
n
(graph theory) A number of edges in a graph.
n
(mathematics) A kind of graph in which most nodes are not neighbors but most can be reached from every other by a small number of steps, i.e. the typical distance between two randomly chosen nodes grows proportionally to the logarithm of the number of nodes in the network.
n
(graph theory) The problem of finding the longest possible induced path in a hypercube.
n
(mathematics) A graph in which every node has three branches, and the edges cannot be coloured in fewer than four colours without two edges of the same colour meeting at a point.
n
(graph theory) A tree structure which includes all vertices of a graph.
n
(graph theory) A graph that is a sparse version of another.
n
(mathematics) A graph (set of connected points) that has one vertex of degree at least three, and all other vertices of degree two or less
n
Alternative form of spider graph [(mathematics) A graph (set of connected points) that has one vertex of degree at least three, and all other vertices of degree two or less]
n
(graph theory) A union of uniform spanning trees.
n
(graph theory) An extra vertex that is not a member of the input.
n
(graph theory) The minimum-weight connected subgraph of a graph that includes all the vertices of that graph.
adj
(graph theory) Of a directed graph, such that for every pair of vertices u and v there is a directed path either from u to v or from v to u.
n
(graph theory) Given a directed graph, a maximal strongly connected subgraph.
n
(mathematics) A subset of a fan (part of a tree).
n
(mathematics) A tree in which the value of a node is equal to the sum of its subnodes
n
(mathematics) A graph such that there exists one or more paths between pairs of vertices in each of two subsets of vertices
adj
(graph theory, of a graph) Whose every minimum vertex cut leads to isolated vertices.
n
(mathematics) A vertex formed by merging two existing verticies of a graph by removing their connecting edge
n
(computing theory) An algorithm for finding two disjoint paths in a non-negatively-weighted directed graph, so that both paths connect the same pair of vertices and have minimum total length.
n
(graph theory) An algorithm for finding the strongly connected components (SCCs) of a directed (connected) graph by utilizing the depth-first search function.
n
(graph theory) An embedding of a graph in the plane, such that each edge is a Jordan arc and every pair of edges meet once.
n
(graph theory) A digraph obtained by assigning a direction to each edge in an undirected complete graph.
n
(mathematics) The sum of the diagonal elements of a square matrix.
n
(graph theory) A connected graph with no cycles or, if the graph is finite, equivalently a connected graph with n vertices and n−1 edges.
n
(graph theory) A complete multipartite graph T(n,r) formed by partitioning a set of n vertices into r subsets, with sizes as equal as possible, and connecting two vertices by an edge if and only if they belong to different subsets.
n
(graph theory) A matrix used to determine whether all of the edges of a graph can be traversed without visiting a vertex more than once.
adj
(algebra) Whose salient properties apply when (the specified object) appears on either side of a given binary operator.
n
(mathematics, order theory) A filter (subset of a poset) that is maximal as a set with respect to the definition of proper filter.
n
(mathematics) A generalization of a directed graph in which the source of an edge is a set of vertices rather than a single vertex.
n
(graph theory) A graph in which the edges are not ordered, so the edge (a, b) is identical to the edge (b, a).
n
(graph theory) In a directed graph, a path in which the edges are not all oriented in the same direction.
n
(graph theory) The graph K_(3,3), which has six vertices in two sets of three and nine edges such that every vertex in one set is connected to each vertex in the other.
n
(graph theory) The number of edges connected to a vertex in a graph.
n
(graph theory) One of the elements of a graph joined or not by edges to other vertices.
n
(graph theory) a set of vertices which touch all the edges of a graph
n
(graph theory) A sequence of alternating vertices and edges, where each edge's endpoints are the preceding and following vertices in the sequence.
n
(graph theory) A graph with only one vertex.
adj
(graph theory, of a graph) having values assigned to its edges
n
(graph theory) A graph that associates a weight (usually a real number) with every edge in the graph.
n
(graph theory) An unsolved problem in mathematics, asking for the largest possible number of edges in a bipartite graph that has a given number of vertices and has no complete bipartite subgraphs of a given size.
n
(mathematical analysis) A k-cell which is a Cartesian product of half-closed intervals which are closed at their infima and open at their suprema, and such that the infimum of each interval is the coordinate of a given point (called "the corner" of the δ-box), and the length (i.e., measure) of each interval is equal to (the given value) δ.
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