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Undirected, connected, and acyclic graph
in-tree. A rooted tree itself has been defined by some authors as a directed graph. A rooted forest is a disjoint union of rooted trees. A rooted forest may
Tree_(graph_theory)
in graph theory, a rooted graph is a graph in which one vertex has been distinguished as the root. Both directed and undirected versions of rooted graphs
Rooted_graph
Graph with oriented edges
weighted directed graphs where two nodes are distinguished, a source and a sink. Rooted directed graphs (also known as flow graphs) are digraphs in which
Directed_graph
Binary operation performed on graphs
In mathematical graph theory, the rooted product (or comb product) of a graph G and a rooted graph H is defined as follows: take |V(G)| copies of H, and
Rooted_product_of_graphs
Directed graph where every node has exactly one path to it from the root
is thus the directed-graph form of a rooted tree, understood here as an undirected graph. An arborescence is also a directed rooted tree in which all edges
Arborescence_(graph_theory)
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
Glossary_of_graph_theory
Directed graph with no directed cycles
In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it
Directed_acyclic_graph
Procedures for constructing new graphs in graph theory
graph from an initial one by a complex change, such as: transpose graph; complement graph; line graph; graph minor; graph rewriting; power of graph;
Graph_operations
Object in graph theory
In the mathematical subfield of graph theory a level structure of a rooted graph is a partition of the vertices into subsets that have the same distance
Level_structure
Bijection between the vertex set of two graphs
root of the rooted tree, etc. The notion of "graph isomorphism" allows us to distinguish graph properties inherent to the structures of graphs themselves
Graph_isomorphism
Graphical representation of a computer program or algorithm
In computer science, a control-flow graph (CFG) is a representation, using graph notation, of all paths that might be traversed through a function during
Control-flow_graph
Topics referred to by the same term
Flow graph may refer to: Flow or rooted graph (graph theory), a graph in which a vertex has been distinguished as the root Control-flow graph (computer
Flow_graph
Trail in a graph that visits each edge once
In graph theory, an Eulerian trail (or Eulerian path) is a trail in a finite graph that visits every edge exactly once (allowing for revisiting vertices)
Eulerian_path
Edge whose deletion would disconnect a graph
In graph theory, a bridge, isthmus, cut-edge, or cut arc is an edge of a graph whose deletion increases the graph's number of connected components. Equivalently
Bridge_(graph_theory)
Measure of similarity between two graphs
graph edit distances between suitably constrained graphs. Likewise, graph edit distance is also a generalization of tree edit distance between rooted
Graph_edit_distance
Linked node hierarchical data structure
be non-empty): A rooted tree with the "away from root" direction (a more narrow term is an "arborescence"), meaning: A directed graph, whose underlying
Tree_(abstract_data_type)
Number of spanning trees of a complete graph
sequences of directed edges that can be added to an empty graph on n vertices to form from it a rooted tree; see Double counting (proof technique) § Counting
Cayley's_formula
Visualization of node-link graphs
Graph drawing is an area of mathematics and computer science combining methods from geometric graph theory and information visualization to derive two-dimensional
Graph_drawing
Limited form of tree data structure
undirected, rather than directed graph, in which case a binary tree is an ordered, rooted tree. Some authors use rooted binary tree instead of binary tree
Binary_tree
Graph formed by complementation and disjoint union
In graph theory, a cograph, or complement-reducible graph, or P4-free graph, is a graph that can be generated from the single-vertex graph K1 by complementation
Cograph
Formula for number of orbits of a group action
F(t)=t^{6}+t^{5}+2t^{4}+3t^{3}+2t^{2}+t+1.} These graphs are shown at the right. The set T3 of rooted ternary trees consists of rooted trees where every node (or non-leaf
Pólya_enumeration_theorem
Infinite graph containing all countable graphs
In the mathematical field of graph theory, the Rado graph, Erdős–Rényi graph, or random graph is a countably infinite graph that can be constructed (with
Rado_graph
Set of all possible values of a system
factor is important structure of the space, see also graph theory: directionality of arcs tree rooted graph For example, the Vacuum World has a branching factor
State space (computer science)
State_space_(computer_science)
Bivariegated graph Cage (graph theory) Cayley graph Circle graph Clique graph Cograph Common graph Complement of a graph Complete graph Cubic graph Cycle graph De
List_of_graph_theory_topics
Trees with additional directed half edges
Blossom trees can be used to sample random planar graphs. A blossom tree is constructed from a rooted tree embedded in the plane by adding opening and
Blossom_tree_(graph_theory)
Length of shortest path between two nodes of a graph
mathematical field of graph theory, the distance between two vertices in a graph is the number of edges in a shortest path (also called a graph geodesic) connecting
Distance_(graph_theory)
Mathematical pen-and-paper game
stalks. The last possible set of graphs that can be made are convergent ones, also known as arbitrarily rooted graphs. By using the fusion principle, we
Hackenbush
Regular graph with girth more than twice its diameter
Does a Moore graph with girth 5 and degree 57 exist? More unsolved problems in mathematics In graph theory, a Moore graph is a regular graph whose girth
Moore_graph
Graph algorithm
components algorithm is an algorithm in graph theory for finding the strongly connected components (SCCs) of a directed graph. It runs in linear time, matching
Tarjan's strongly connected components algorithm
Tarjan's_strongly_connected_components_algorithm
Algorithm for the directed version of the minimum spanning tree problem
In graph theory, Edmonds' algorithm or Chu–Liu/Edmonds' algorithm is an algorithm for finding a spanning arborescence of minimum weight (sometimes called
Edmonds'_algorithm
Graph linking pairs of comparable elements in a partial order
Therefore, permutation graphs are another subclass of comparability graphs. The trivially perfect graphs are the comparability graphs of rooted trees. Cographs
Comparability_graph
On tangency patterns of circles
that unbiased limit graphs of bounded-degree planar rooted graphs are almost surely recurrent, meaning that random walks on these graph limits almost surely
Circle_packing_theorem
Intersection graph of unit intervals on the real line
In graph theory, a branch of mathematics, an indifference graph is an undirected graph constructed by assigning a real number to each vertex and connecting
Indifference_graph
Tree which includes all vertices of a graph
of graph theory, a spanning tree T of an undirected graph G is a subgraph that is a tree which includes all of the vertices of G. In general, a graph may
Spanning_tree
Generalization of depth-first search trees
the graph shown below, the tree with edges 1–3, 2–3, and 3–4 is a Trémaux tree when it is rooted at vertex 1 or vertex 2: every edge of the graph belongs
Trémaux_tree
Graph with equal-size maximal independent sets
number of edges. If G is any n-vertex graph, then the rooted product of G with a one-edge graph (that is, the graph H formed by adding n new vertices to
Well-covered_graph
Branching diagram of evolutionary relationships between organisms
strictly speaking a tree, but rather a more general graph, or a directed acyclic graph in the case of rooted networks. They are used to overcome some of the
Phylogenetic_tree
Mathematical function
odd values of n counts Perfect matchings of the complete graph Kn + 1 for odd n. In such a graph, any single vertex v has n possible choices of vertex that
Double_factorial
Finite sets whose elements are all hereditarily finite sets
structure. In graph theory, the graph whose vertices correspond to hereditarily finite sets and edges correspond to set membership is the Rado graph or random
Hereditarily_finite_set
Type of graph in mathematics
multitree may describe either of two equivalent structures: a directed acyclic graph (DAG) in which there is at most one directed path between any two vertices
Multitree
directed acyclic graph (PDAG) is a data structure that is used to represent a Boolean function. A Boolean function can be represented as a rooted, directed acyclic
Propositional directed acyclic graph
Propositional_directed_acyclic_graph
Graph without four-vertex star subgraphs
In graph theory, an area of mathematics, a claw-free graph is a graph that does not have a claw as an induced subgraph. A claw is another name for the
Claw-free_graph
Type of graph in mathematics
1987 by Rebane and Pearl. An arborescence is a directed rooted tree, i.e. a directed acyclic graph in which there exists a single source node that has a
Polytree
Graph used to visualize evolutionary relationships, including reticulation events
built from (hybridization networks, usually built from rooted trees, ancestral recombination graphs (ARGs) from binary sequences, median networks from a
Phylogenetic_network
Well-quasi-ordering of finite trees
transfinite recursion). In 2004, the result was generalized from trees to graphs as the Robertson–Seymour theorem, a result that has also proved important
Kruskal's_tree_theorem
orientation of the remaining edges in the graph. For this reason, there are exactly 2n −3 times as many full rooted binary trees with n leaves as there are
Unrooted_binary_tree
Type of proof technique
directed edges that can be added to an empty graph on n {\displaystyle n} vertices to form from it a rooted tree. The directed edges point away from the
Double counting (proof technique)
Double_counting_(proof_technique)
Binary operation on graphs
graph theory, a graph product is a binary operation on graphs. Specifically, it is an operation that takes two graphs G1 and G2 and produces a graph H
Graph_product
Graph where every connected induced subgraph has a universal vertex
In graph theory, a trivially perfect graph is a graph with the property that in each of its induced subgraphs the size of the maximum independent set equals
Trivially_perfect_graph
Tree node with two other nodes as descendants
In graph theory and computer science, the lowest common ancestor (LCA) (also called least common ancestor) of two nodes v and w in a tree or directed
Lowest_common_ancestor
Chordal graph where all cycles of even length have odd chords
interval graphs and the larger class of rooted directed path graphs are leaf powers. Since strongly chordal graphs are both chordal graphs and dually
Strongly_chordal_graph
In the mathematical field of graph theory, a word-representable graph is a graph that can be characterized by a word (or sequence) whose entries alternate
Word-representable_graph
On the number of spanning trees in a graph
mathematical field of graph theory, Kirchhoff's theorem or Kirchhoff's matrix tree theorem is a theorem about the number of spanning trees in a graph. It states
Kirchhoff's_theorem
Infinite dimensional Lie group
problem-oriented work can lead to far-reaching conceptual results. A rooted tree is a graph with a distinguished node, called the root, in which every other
Butcher_group
Search algorithm
Monte-Carlo method to bias search into the largest Voronoi regions of a graph in a configuration space. Some variations can even be considered stochastic
Rapidly_exploring_random_tree
A family of simple undirected graphs defined by spectral properties
In graph theory, a nut graph is a finite simple graph on at least two vertices whose adjacency matrix has nullity one and whose kernel is spanned by a
Nut_graph_(graph_theory)
Way of representing the hierarchical nature of a structure in a graphical form
(data structure) for computer science; insofar as it relates to graph theory, see tree (graph theory) or tree (set theory). Other related articles are listed
Tree_structure
Graph-theoretic description of polyhedra
planar graph, and every 3-connected planar graph can be represented as the graph of a convex polyhedron. For this reason, the 3-connected planar graphs are
Steinitz's_theorem
Mathematical concept
isomorphic when there exists a graph isomorphism between them which preserves the leaf labels. In the case of rooted X-trees, the isomorphism must also
Agreement_forest
Programming paradigm focused on difficult search problems
r s Answer: 6 Stable Model: r q s An n {\displaystyle n} -coloring of a graph G = ⟨ V , E ⟩ {\displaystyle G=\left\langle V,E\right\rangle } is a function
Answer_set_programming
mathematics, a minimum bottleneck spanning tree (MBST) in an undirected graph is a spanning tree in which the most expensive edge is as cheap as possible
Minimum bottleneck spanning tree
Minimum_bottleneck_spanning_tree
Fewest graph edges whose removal breaks all cycles
with a (possibly trivial) tree rooted at each vertex. Several authors have studied the parameterized complexity of graph algorithms on r-near-trees, parameterized
Cyclomatic_number
Recursively splitting a graph into subsets of nodes
In graph theory, the modular decomposition is a decomposition of a graph into subsets of vertices called modules. A module is a generalization of a connected
Modular_decomposition
the mathematics of infinite graphs, an end of an undirected graph represents, intuitively, a direction in which the graph extends to infinity. Ends may
End_(graph_theory)
Data structure for Boolean functions
propositional directed acyclic graphs (PDAG). A Boolean function can be represented as a rooted, directed, acyclic graph, which consists of several (decision)
Binary_decision_diagram
Notation for tree data structures
Newick notation or New Hampshire tree format) is a way of representing graph-theoretical trees with edge lengths using parentheses and commas. It was
Newick_format
Natural number
parenthesizing five items. The largest graceful graph on 14 nodes has exactly 68 edges. There are 68 different undirected graphs with six edges and no isolated nodes
68_(number)
Study of graphs as a representation of relations between discrete objects
science, and network science, network theory is a part of graph theory. It defines networks as graphs where the vertices or edges possess attributes. Network
Network_theory
Vertex adjacent to all others in a graph
set. The wheel graphs may be formed by adding a universal vertex to a cycle graph. The trivially perfect graphs are obtained from rooted trees by adding
Universal_vertex
Hydra game in mathematical logic
In mathematics, especially mathematical logic, graph theory and number theory, the Buchholz hydra game is a type of hydra game, which is a single-player
Buchholz_hydra
Topics referred to by the same term
rather than arbitrary infinite trees are admitted) Tree (graph theory), a connected undirected graph without simple cycles Tree (set theory), a generalization
Infinite_tree
Square matrix containing the distances between elements in a set
In mathematics, computer science and especially graph theory, a distance matrix is a square matrix (two-dimensional array) containing the distances, taken
Distance_matrix
Form taken by the network of interconnections of a circuit
proposed by Chen in 1965. Chen's method is based on a rooted tree. Another way of extending classical graph theory for active components is through the use
Circuit_topology_(electrical)
Partial order with well-ordered predecessors
be viewed as rooted trees in the sense of graph theory in one of two ways: either as a tree (graph theory) or as a trivially perfect graph. In the first
Tree_(set_theory)
On linear-time algorithms for graph logic
study of graph algorithms, Courcelle's theorem is the statement that every graph property definable in the monadic second-order logic of graphs can be decided
Courcelle's_theorem
Algorithm for two disjoint paths in a graph
a weighted graph G. Figure B calculates the shortest path P1 from A to F (A–B–D–F). Figure C illustrates the shortest path tree T rooted at A, and the
Suurballe's_algorithm
Type of transfinite numbers
the hydra theorem, which represents decreasing sequences of ordinals as a graph-theoretic game. The fixed points of the "epsilon mapping" x ↦ ε x {\displaystyle
Epsilon_number
Integer matrices with +1 or −1 determinant; invertible over the integers. GL_n(Z)
balanced signed graph; thus, this example says that the incidence matrix of a signed graph is totally unimodular if the signed graph is balanced. The
Unimodular_matrix
(AMR) is a semantic representation language. AMR graphs are rooted, labeled, directed, acyclic graphs (DAGs), comprising whole sentences. They are intended
Abstract Meaning Representation
Abstract_Meaning_Representation
Non-hierarchical interaction of overlapping document markup entities
develop corpus management systems on the basis of graph data bases and for using established graph-based formalisms as pivot formats. For implementing
Overlapping_markup
Academic field
foundation of graph theory, a branch of mathematics that studies the properties of pairwise relations in a network structure. The field of graph theory continued
Network_science
secular state with increasing vigour after Recep Tayyip Erdoğan's Islamist-rooted Justice and Development Party (AKP) came into power in 2002. While the state
Religion_in_Turkey
stands for the ordered pairs of vertices, called arcs or edges. A rooted tree is a graph in which any two vertices are connected by exactly one simple path
Irrigation_game
Graph representing leaves of a given tree graph
interval graphs and the larger class of rooted directed path graphs are leaf powers. The indifference graphs are exactly the leaf powers whose underlying
Leaf_power
Collection of open-source Python software tools for computational biology
changing a tree's root, and analysing branch features such as length or score. Rooted trees can be drawn in ASCII or using matplotlib (see Figure 1), and the
Biopython
Any planar graph can be subdivided by removing a few vertices
In graph theory, the planar separator theorem is a form of isoperimetric inequality for planar graphs, that states that any planar graph can be split
Planar_separator_theorem
Tree data structure in which each node has at most m children
In graph theory, an m-ary tree (for nonnegative integers m) (also known as n-ary, k-ary, k-way or generic tree) is an arborescence (or, for some authors
M-ary_tree
= number of irredundant sets in the 29-cocktail party graph 1713 = number of aperiodic rooted trees with 12 nodes 1714 = number of regions formed by
1000_(number)
In backtracking algorithms, technique that reduces search space
retracted from, their sets are automatically ignored. The rationale of graph-based backjumping is that a safe jump can be found by checking which of
Backjumping
Graph formed by subdivision of triangles
the graph into three interleaved trees rooted at the three vertices of the exterior face. The Apollonian networks do not form a family of graphs that
Apollonian_network
Natural number
11130 and 77711; number of regular simple graphs spanning 7 vertices 932 = 22 × 233, number of regular simple graphs on 7 labeled nodes 933 = 3 × 311 934 =
900_(number)
Algorithm in graph theory
In mathematical optimization, the network simplex algorithm is a graph theoretic specialization of the simplex algorithm. The algorithm is usually formulated
Network_simplex_algorithm
Examination of the heart's electrical activity
shows a line graph of the heart's electrical activity through repeated cardiac cycles. It is an electrogram of the heart which is a graph of voltage versus
Electrocardiography
Jericho, Greg (October 28, 2022). "Taylor Swift's incredible success in graphs – who can blame me for being a Swiftie as a 50-year-old man?". The Guardian
Cultural impact of Taylor Swift
Cultural_impact_of_Taylor_Swift
Representation of a graph as a path graph "thickened" by some amount
In graph theory, a path decomposition of a graph G is, informally, a representation of G as a "thickened" path graph, and the pathwidth of G is a number
Pathwidth
Set system used in greedy optimization
directed graph D rooted at r. Let the ground set be the (directed) edges of D and the feasible sets be the edge sets of each directed subtree rooted at r
Greedoid
previously negative development-fertility association is reversed; the graph becomes J-shaped. Myrskylä et al. contend that there has occurred "a fundamental
Income_and_fertility
Square matrix without an inverse
or apply forces in certain directions. In graph theory and network physics, the Laplacian matrix of a graph is inherently singular (it has a zero eigenvalue)
Singular_matrix
Spanning tree type
Capacitated minimum spanning tree is a minimal cost spanning tree of a graph that has a designated root node r {\displaystyle r} and satisfies the capacity
Capacitated minimum spanning tree
Capacitated_minimum_spanning_tree
Theory in computer science
complete. the structure semantics. We label states. QCTL* = QCTL = MSO over graphs. Model checking is PSPACE-complete but satisfiability is undecidable. A
Computation_tree_logic
ROOTED GRAPH
ROOTED GRAPH
Male
Polish
Pet form of Polish Rościsław, ROSTEK means "usurp-glory."
Surname or Lastname
English
English : unexplained.
Boy/Male
Gaelic Irish
Red haired.
Girl/Female
Arabic
Ruby; Precious Stone
Girl/Female
Muslim
Spiritual. Of spirit.
Surname or Lastname
English
English : variant of Rosson.Norwegian : habitational name from any of several farmsteads named Rosten or Røsten, from rust ‘grove’, ‘ridge’.Americanized form of one or more like-sounding Jewish surnames. Compare Rothstein.
Surname or Lastname
English
English : variant of Roots.
Boy/Male
Indian
Season
Girl/Female
Arabic
Of Spirit
Surname or Lastname
English
English : habitational name from any of the extremely numerous places named with Old English wudu ‘wood’ + tūn ‘enclosure’, ‘settlement’, such as Wootton in Northamptonshire or Oxfordshire, Wootton Bassett in Wiltshire, Wotton in Surrey, and Wotton under Edge in Gloucestershire.
Boy/Male
Muslim
Deep-rooted. Stable.
Boy/Male
Arabic, Australian, British, English
Deep Rooted
Male
Finnish
Short form of Finnish Roopertti, ROOPE means "bright fame."
Girl/Female
Hindu, Indian
Durga Devi
Female
Hebrew
(רï‹×ªÖ¶×) Hebrew unisex name derived from the word rethem, found in the bible, ROTEM means "juniper" or "broom plant," a shrub growing in the deserts of Arabia with yellowish flowers, and a bitter root which the poor were accustomed to eat.Â
Boy/Male
Arabic, Indian, Muslim
Firmly Rooted
Surname or Lastname
English
English : patronymic from Root 1.
Surname or Lastname
English (Norfolk and Suffolk)
English (Norfolk and Suffolk) : topographic name for someone who lived at the foot of a hill.
Surname or Lastname
English (Sussex)
English (Sussex) : unexplained.
Surname or Lastname
English
English : variant of Rocker.
ROOTED GRAPH
ROOTED GRAPH
Boy/Male
Sikh
Only one creator
Boy/Male
Tamil
Country
Boy/Male
German
Peace
Girl/Female
American, Christian, Hebrew, Hindu, Indian, Tamil
Gracious; Grace; Offering with Both Ends; Favour
Surname or Lastname
English
English : occupational name for a watchman or guard, from Old English weard ‘guard’ (used as both an agent noun and an abstract noun).Irish : reduced form of McWard, an Anglicized form of Gaelic Mac an Bhaird ‘son of the poet’. The surname occurs throughout Ireland, where three different branches of the family are known as professional poets.Surname adopted by bearers of the Jewish surname Warshawski, Warshawsky or some other Jewish name bearing some similarity to the English name.Americanized form of French Guerin.The surname Ward was brought to North America from England independently by several different bearers in the 17th and 18th centuries. Nathaniel Ward (1578–1652), author of the MA legal code, was born in Haverhill, Suffolk, England, and emigrated to Agawam (Ipswich, MA) in 1633. William Ward was one of the original settlers of Sudbury, MA, in about 1638. Miles Ward came from England to Salem, MA, in about 1639. Thomas Ward (d. 1689) settled in Newport, RI, in 1671; among his descendants were two governors of colonial RI.
Boy/Male
Russian
Great.
Biblical
admiration; perfection; consummation
Girl/Female
American, Australian, British, English, German, Greek, Irish, Latin
Follower of Christ; Anointed; Variant of Christian; Christian
Boy/Male
Hindu, Indian
God Shiva
Boy/Male
French, German, Hebrew, Italian
God has Healed; Form of Raphael
ROOTED GRAPH
ROOTED GRAPH
ROOTED GRAPH
ROOTED GRAPH
ROOTED GRAPH
a.
Firm-footed; determined.
a.
Feather-footed; as, a rough-footed dove.
a.
Hood-shaped; esp. (Bot.), rolled up like a cornet of paper; cuculate, as the spethe of the Indian turnip.
a.
False; dishonest; fraudulent; as, crooked dealings.
a.
Having a hoodlike crest or prominence on the head or neck; as, the hooded seal; a hooded snake.
a.
Rooted
a.
Having webbed feet; palmiped; as, a goose or a duck is a web-footed fowl.
a.
Hooked or crooked in an extreme degree.
a.
Rooted in the heart.
a.
Alt. of Cloven-hoofed
a.
Not liable to stumble or fall; as, a sure-footed horse.
a.
Having the form of a hook; curvated; as, the hooked bill of a bird.
a.
Having leaflike expansions on the legs; -- said of certain insects; as, the leaf-footed bug (Leptoglossus phyllopus).
a.
Slow-footed.
a.
Having wings attached to the feet; as, wing-footed Mercury; hence, swift; moving with rapidity; fleet.
v. i.
To take root; to become rooted.
a.
Not yet roofed.
a.
Wearing boots, especially boots with long tops, as for riding; as, a booted squire.
a.
Covered with hoarfrost or anything resembling hoarfrost; ornamented with frosting; also, frost-bitten; as, a frosted cake; frosted glass.
a.
Having a white front; as, the white-fronted lemur.