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Sequence of edges which join a sequence of vertices on a given graph
In graph theory, a path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices which, by most definitions, are all distinct
Path_(graph_theory)
Graph with nodes connected linearly
In the mathematical field of graph theory, a path graph (or linear graph) is a graph whose vertices can be listed in the order v1, v2, ..., vn such that
Path_graph
Set of edges without common vertices
In the mathematical discipline of graph theory, a matching or independent edge set in an undirected graph is a set of edges without common vertices. In
Matching_(graph_theory)
Computational problem of graph theory
In 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
Shortest_path_problem
Vertices connected in pairs by edges
In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a set of objects where some pairs of the objects are in some
Graph_(discrete_mathematics)
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
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)
Path in a graph that visits each vertex exactly once
the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly
Hamiltonian_path
Graph with oriented edges
In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is made up of a set of vertices connected by directed
Directed_graph
Basic concept of graph theory
mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need
Connectivity_(graph_theory)
Problem of finding a cycle through all vertices of a graph
Hamiltonian path problem is a topic discussed in the fields of complexity theory and graph theory. It decides if a directed or undirected graph, G, contains
Hamiltonian_path_problem
Undirected, connected, and acyclic graph
In graph theory, a tree is an undirected graph in which every pair of distinct vertices is connected by exactly one path, or equivalently, a connected
Tree_(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
Maximal subgraph whose vertices can reach each other
In graph theory, a component of an undirected graph is a connected subgraph that is not part of any larger connected subgraph. The components of any graph
Component_(graph_theory)
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
Longest distance between two vertices
In graph theory, the diameter of a connected undirected graph is the farthest distance between any two of its vertices. That is, it is the diameter of
Diameter_(graph_theory)
Problem of finding the longest simple path for a given graph
In graph theory and theoretical computer science, the longest path problem is the problem of finding a simple path of maximum length in a given graph. A
Longest_path_problem
Graph whose embedding in a Euclidean space forms a regular tiling
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}
Lattice_graph
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)
A family of simple undirected graphs defined by spectral properties
In graph theory, a nut graph is a finite simple graph with at least two vertices whose adjacency matrix has nullity one and whose kernel is spanned by
Nut_graph_(graph_theory)
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
as vertex and path, see Glossary of graph theory. For links to existing articles about particular kinds of graphs, see Category:Graphs. Some of the finite
List_of_graphs
Partition of a graph's nodes into 2 disjoint subsets
In graph theory, a cut is a partition of the vertices of a graph into two disjoint subsets. Any cut determines a cut-set, the set of edges that have one
Cut_(graph_theory)
On bipartite matching and vertex cover
In the mathematical area of graph theory, Kőnig's theorem, proved by Dénes Kőnig (1931), describes an equivalence between the maximum matching problem
Kőnig's theorem (graph theory)
Kőnig's_theorem_(graph_theory)
Type of graph in mathematical graph theory
discipline of graph theory, the (m,n)-lollipop graph is a special type of graph consisting of a complete graph (clique) on m vertices and a path graph on n vertices
Lollipop_graph
Partition of a graph whose components are reachable from all vertices
In the mathematical theory of directed graphs, a graph is said to be strongly connected if every vertex is reachable from every other vertex. The strongly
Strongly_connected_component
Topics referred to by the same term
to a metric space or a topological space Simple path (graph theory), a simple path is a path in a graph which does not have repeating vertices This disambiguation
Simple_path
Subgraph with contracted edges
In graph theory, an undirected graph H is called a minor of the undirected graph G if H can be formed from G by deleting edges and vertices and by contracting
Graph_minor
Directed graph where edges have a capacity
In graph theory, a flow network (also known as a transportation network) is a directed graph where each edge has a capacity and each edge receives a flow
Flow_network
Deleting a graph edge and merging its nodes
In graph theory, an edge contraction is an operation that removes an edge from a graph while simultaneously merging the two vertices that it previously
Edge_contraction
Graph generated by a random process
The theory of random graphs lies at the intersection between graph theory and probability theory. From a mathematical perspective, random graphs are used
Random_graph
Fundamental unit of which graphs are formed
specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set
Vertex_(graph_theory)
Area of discrete mathematics
computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context
Graph_theory
discrete and Euclidean geometries, graph theory, group theory, mathematical logic, number theory, set theory, Ramsey theory, dynamical systems, and partial
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Topics referred to by the same term
executable programs Path (graph theory), a sequence of edges of a graph st-connectivity problem, sometimes known as the "path problem" Path (topology), a continuous
Path
Cubic graph with 10 vertices and 15 edges
bridgeless graph has a cycle-continuous mapping to the Petersen graph. More unsolved problems in mathematics In the mathematical field of graph theory, the
Petersen_graph
Trail in which only the first and last vertices are equal
In graph theory, a cycle in a graph is a non-empty trail in which only the first and last vertices are equal. A directed cycle in a directed graph is
Cycle_(graph_theory)
Study of graphs defined by geometric means
Geometric graph theory in the broader sense is a large and amorphous subfield of graph theory, concerned with graphs defined by geometric means. In a stricter
Geometric_graph_theory
Connected series of line segments
points within a polygon Piecewise regression Path (graph theory), an analogous concept in abstract graphs Polyhedral terrain, a 3D generalization of a
Polygonal_chain
Graph path which is an induced subgraph
In the mathematical area of graph theory, an induced path in an undirected graph G is a path that is an induced subgraph of G. That is, it is a sequence
Induced_path
Algorithm for finding shortest paths
DYKE-strəz) is an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent, for example, a road network. It was
Dijkstra's_algorithm
Graph whose biconnected components are all cliques
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
Block_graph
Number of edges touching a vertex in a graph
In graph theory, the degree (or valency) of a vertex of a graph is the number of edges that are incident to the vertex; in a multigraph, a loop contributes
Degree_(graph_theory)
Graph with nodes connected in a closed chain
In graph theory, a cycle graph or circular graph is a graph that consists of a single cycle, or in other words, some number of vertices (at least 3, if
Cycle_graph
Directed graph where each vertex pair has one arc
In graph theory, a tournament is a directed graph with exactly one edge between each two vertices, in one of the two possible directions. Equivalently
Tournament_(graph_theory)
Assigning directions to the edges of an undirected graph
In graph theory, an orientation of an undirected graph is an assignment of a direction to each edge, turning the initial graph into a directed graph. A
Orientation_(graph_theory)
Graph representing edges of another graph
In 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
Line_graph
Graph defined from a mathematical group
geometric group theory. The structure and symmetry of Cayley graphs make them particularly good candidates for constructing expander graphs. Let G {\displaystyle
Cayley_graph
Partition of graph into sequence of paths
In graph theory, an ear of an undirected graph G is a path P where the two endpoints of the path may coincide, but where otherwise no repetition of edges
Ear_decomposition
Planar, undirected graph with 2n vertices and 3n-2 edges
mathematical field of graph theory, the ladder graph Ln is a planar, undirected graph with 2n vertices and 3n − 2 edges. The ladder graph can be obtained as
Ladder_graph
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
Square matrix used to represent a graph or network
In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether
Adjacency_matrix
Operation that combines two graphs
In graph theory, the join operation is a graph operation that combines two graphs by connecting every vertex of one graph to every vertex of the other
Join_(graph_theory)
Graph representing faces of another graph
mathematical discipline of graph theory, the dual graph of a planar graph G is a graph that has a vertex for each face of G. The dual graph has an edge for each
Dual_graph
Binary operation in graph theory
In graph theory, the strong product is a way of combining two graphs to make a larger graph. Two vertices are adjacent in the strong product when they
Strong_product_of_graphs
Mathematical theory on behavior of connected clusters in a random graph
degree distribution follows a power law Shortest path problem – Computational problem of graph theory Swiss cheese model – Model used in risk analysis
Percolation_theory
Graph with a median for each three vertices
In graph theory, a division of mathematics, a median graph is an undirected graph in which every three vertices a {\displaystyle a} , b {\displaystyle
Median_graph
Longest distance between tree vertices
In graph theory, the triameter is a metric invariant that generalizes the concept of a graph's diameter. It is defined as the maximum sum of pairwise
Triameter_(graph_theory)
Sparse graph with strong connectivity
In graph theory, an expander graph is a sparse graph that has strong connectivity properties, quantified using vertex, edge or spectral expansion. Expander
Expander_graph
Graph with same nodes as but complementary connections to another
In the mathematical field of graph theory, the complement or inverse of a graph G is a graph H on the same vertices such that two distinct vertices are
Complement_graph
Classic problem in graph theory
of impossibility by Leonhard Euler, in 1736, laid the foundations of graph theory and foreshadowed the idea of topology. The city of Königsberg in Prussia
Seven_Bridges_of_Königsberg
Problem in graph theory
finite connected vertex-transitive graph contain a Hamiltonian path? More unsolved problems in mathematics In graph theory, the Lovász conjecture (1969) is
Lovász_conjecture
Graph with all vertices of degree 3
of graph theory, a cubic graph is a graph in which all vertices have degree three. In other words, a cubic graph is a 3-regular graph. Cubic graphs are
Cubic_graph
Plotting by a computer application
path on a weighted graph. Pathfinding is closely related to the shortest path problem, within graph theory, which examines how to identify the path that
Pathfinding
directed graph G = (V, E), a path cover is a set of directed paths such that every vertex v ∈ V belongs to at least one path. Note that a path cover may
Path_cover
Method of graph decomposition
In graph theory, a haven is a certain type of function on sets of vertices in an undirected graph. If a haven exists, it can be used by an evader to win
Haven_(graph_theory)
Graph where all long cycles have a chord
In 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
Chordal_graph
Graph made from vertices and edges of a convex polyhedron
In geometric graph theory, a branch of mathematics, a polyhedral graph is the undirected graph formed from the vertices and edges of a convex polyhedron
Polyhedral_graph
Flow graph invented by Claude Shannon
signal-flow graph theory builds on that of directed graphs (also called digraphs), which includes as well that of oriented graphs. This mathematical theory of
Signal-flow_graph
Property of graphs that depends only on abstract structure
In graph theory, a graph property or graph invariant is a property of graphs that depends only on the abstract structure, not on graph representations
Graph_property
Graph of intervisible locations in computational geometry
obstacles, where it may turn, so the Euclidean shortest path is the shortest path in a visibility graph that has as its nodes the start and destination points
Visibility_graph
3-regular graph with no 3-edge-coloring
In the mathematical field of graph theory, a snark is an undirected graph with exactly three edges per vertex whose edges cannot be colored with only three
Snark_(graph_theory)
Graph in which every two vertices are adjacent
In the mathematical field of graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique
Complete_graph
classes of infinite paths, as havens describing strategies for pursuit–evasion games on the graph, or (in the case of locally finite graphs) as topological
End_(graph_theory)
Graph divided into two independent sets
In 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
Bipartite_graph
Number of vertices with unambiguous distances
In graph theory, the metric dimension of a graph G is the minimum cardinality of a subset S of vertices such that all other vertices are uniquely determined
Metric dimension (graph theory)
Metric_dimension_(graph_theory)
Measure of the structural complexity of a software program
fixing a spanning forest of the graph, and then considering the cycles formed by one edge not in the forest and the path in the forest connecting the endpoints
Cyclomatic_complexity
Directed path algebra
basic reference is the book Leavitt Path Algebras. The theory of Leavitt path algebras uses terminology for graphs similar to that of C*-algebraists, which
Leavitt_path_algebra
Unrelated vertices in graphs
In graph theory, an independent set, stable set, coclique or anticlique is a set of vertices in a graph, no two of which are adjacent. That is, it is a
Independent set (graph theory)
Independent_set_(graph_theory)
Algorithm for finding the shortest paths in graphs
holding the shortest path from the source to each vertex distance := list of size n predecessor := list of size n // Step 1: initialize graph for each vertex
Bellman–Ford_algorithm
Measure of a graph's centrality, based on shortest paths
In graph theory, betweenness centrality is a measure of centrality in a graph based on shortest paths. Betweenness centrality measures how frequently a
Betweenness_centrality
Type of graph in graph theory
mathematical field of graph theory, a graph G is said to be hypohamiltonian if G itself does not have a Hamiltonian cycle but every graph formed by removing
Hypohamiltonian_graph
Path-finding using high-weight graph edges
In graph algorithms, the widest path problem is the problem of finding a path between two designated vertices in a weighted graph, maximizing the weight
Widest_path_problem
Graph with at most one cycle per component
In graph theory, a pseudoforest is an undirected graph in which every connected component has at most one cycle. That is, it is a system of vertices and
Pseudoforest
Graph with sign-labeled edges
In 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
Signed_graph
Graph that can be embedded in the plane
In 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
Planar_graph
When every path in a control-flow graph must go through one node to reach another
In computer science, a node d of a control-flow graph dominates a node n if every path from the entry node to n must go through d. Notationally, this is
Dominator_(graph_theory)
Structure-preserving correspondence between node-link graphs
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
Graph_homomorphism
In mathematics, and, in particular, in graph theory, a rooted graph is a graph in which one vertex has been distinguished as the root. Both directed and
Rooted_graph
Graph of n vertices with a perfect matching for every subgraph of n-1 vertices
In graph theory, a mathematical discipline, a factor-critical graph (or hypomatchable graph) is a graph with an odd number of vertices in which deleting
Factor-critical_graph
On forbidden minors in planar graphs
In graph theory, Wagner's theorem is a mathematical forbidden graph characterization of planar graphs, named after Klaus Wagner, stating that a finite
Wagner's_theorem
Graph which is isomorphic to its complement
of graph theory, a self-complementary graph is a graph which is isomorphic to its complement. The simplest non-trivial self-complementary graphs are
Self-complementary_graph
Graph made from disjoint union of complete graphs
In graph theory, a branch of mathematics, a cluster graph is a graph formed from the disjoint union of complete graphs. Equivalently, a graph is a cluster
Cluster_graph
In the mathematical field of graph theory, the Tutte graph is a 3-regular graph with 46 vertices and 69 edges named after W. T. Tutte. It has chromatic
Tutte_graph
Operation in graph theory
In graph theory, the Cartesian product G □ H of graphs G and H is a graph such that: the vertex set of G □ H is the Cartesian product V(G) × V(H); and
Cartesian_product_of_graphs
Tree graph with all nodes within distance 1 from central path
In graph theory, a caterpillar or caterpillar tree is a tree in which all the vertices are within distance 1 of a central path. Caterpillars were first
Caterpillar_tree
Concept in network topology
geodesic, i.e., the longest shortest path between any two nodes in the network (see Distance (graph theory)). The average path length distinguishes an easily
Average_path_length
Graphs formed by a hypercube's edges and vertices
In graph theory, the hypercube graph Q n {\displaystyle Q_{n}} is the edge graph of the n {\displaystyle n} -dimensional hypercube, that is, it is the
Hypercube_graph
Two closely related models for generating random graphs
the mathematical field of graph theory, the Erdős–Rényi models are two closely related models for generating random graphs and the evolution of a random
Erdős–Rényi_model
Graph representing intersections between given sets
In graph theory, an intersection graph is a graph that represents the pattern of intersections of a family of sets. Any graph can be represented as an
Intersection_graph
PATH GRAPH-THEORY
PATH GRAPH-THEORY
Girl/Female
Arabic, Assamese, Hindu, Indian, Kannada, Malayalam, Marathi, Muslim, Telugu
Grape
Boy/Male
Indian
Grape
Female
English
Short form of English Katherine, KATH means "pure."
Female
Hebrew
(בַּתש×וּעַ) Variant spelling of Hebrew Bath-Shuwa, BATH-SHUA means "daughter of wealth."Â
Female
Hebrew
(בַּת-ש×ֶבַע) Hebrew name BATH-SHEBA means "daughter of the oath." In the bible, this is the name of a wife of Uriah then later King David, and mother of Solomon. Also spelled Bat-Sheva, Bathsheba, and Bathsheva.
Female
English
English short form of French Catherine, CATH means "pure."
Boy/Male
Arabic, Modern
Road; The Way
Girl/Female
Indian
Grape like
Surname or Lastname
English (Bath)
English (Bath) : unexplained.
Girl/Female
Muslim
Grape vine
Male
English
English unisex short form of English Patrick and Latin Patricia, PAT means "patrician; of noble birth."
Girl/Female
Australian, British, English
Way
Female
Hebrew
(בַּתש×וּעַ) Hebrew name BATH-SHUWA means "daughter of wealth." In the bible, this is another name Bath-Sheba is known by.
Surname or Lastname
English (Bristol and Bath)
English (Bristol and Bath) : unexplained.
Surname or Lastname
English
English : habitational name from the city of Bath in western England, which is the site of sumptuous, but in the Middle Ages ruined, Roman baths. The place is named with the dative plural of Old English bæð ‘bath’. In some cases the surname may have originated as a metonymic occupational name for an attendant at a public bath house.Scottish : reduced and altered form of McBeth.German : variant of Bathe.Indian (Panjab) : Sikh name based on the name of a Jat clan.
Surname or Lastname
English (mainly Devon)
English (mainly Devon) : variant of Pate 1.
Boy/Male
Muslim
Grape
Boy/Male
Arabic, Modern
Grape
Male
Irish
Short form of Irish Gaelic Parthalán, possibly PARTH means "son of Talmai."
Surname or Lastname
English and Scottish
English and Scottish : from the personal name Pat(t), Pate, a short form of Patrick.English and Scottish : nickname for a man with a bald head, from Middle English pate ‘head’, ‘skull’.French (Paté) : from Old French pat(t)é ‘with paws’, ‘pawed’ (from pat(t)e ‘paw’), a nickname, applied presumably to a man with large and clumsy hands and feet.German : nickname for a trustworthy man, from Middle High German pate, Middle Low German pade ‘godfather’, ‘male relative’ (see Paeth), or alternatively from a personal name Bado, probably meaning ‘battle’, ‘fight’.
PATH GRAPH-THEORY
PATH GRAPH-THEORY
Boy/Male
American, British, English
From Bart's Meadow
Girl/Female
Indian, Modern, Sikh
Love
Female
Basque
, miracle.
Girl/Female
African, Arabic, Australian, German, Hindu, Indian, Marathi, Muslim, Swahili, Tamil
Happiness; Radiant; Luminous; Brilliant; Illuminating; Angry Bird; Bright and Shining
Girl/Female
Australian, Hebrew, Jewish
Plant; Flower
Girl/Female
American, Australian, British, Christian, English, French, Greek, Hebrew, Italian, Latin
Bright; Clear; Similar to the Latin Clara; Famous
Girl/Female
Christian, Hindu, Indian, Marathi, Sanskrit
Lovely
Boy/Male
Indian, Kannada
Voluminous
Girl/Female
Hindu
The light of india
Girl/Female
Native American
Dance.
PATH GRAPH-THEORY
PATH GRAPH-THEORY
PATH GRAPH-THEORY
PATH GRAPH-THEORY
PATH GRAPH-THEORY
n.
A small piece of anything used to repair a breach; as, a patch on a kettle, a roof, etc.
imp. & p. p.
of Path
n.
A small mass, as of butter, shaped by pats.
adv.
In a pat manner.
pl.
of Path
v. t.
To adorn, as the face, with a patch or patches.
n.
The act of exposing the body, or part of the body, for purposes of cleanliness, comfort, health, etc., to water, vapor, hot air, or the like; as, a cold or a hot bath; a medicated bath; a steam bath; a hip bath.
v. t.
To make a path in, or on (something), or for (some one).
n.
A towing path.
n.
A way, course, or track, in which anything moves or has moved; route; passage; an established way; as, the path of a meteor, of a caravan, of a storm, of a pestilence. Also used figuratively, of a course of life or action.
n.
Fig.: Anything regarded as a patch; a small piece of ground; a tract; a plot; as, scattered patches of trees or growing corn.
pr.p. & vb. n.
of Path
n.
Hence: The which contains the strength of life; the vital or essential part; concentrated force; vigor; strength; importance; as, the speech lacked pith.
v. t.
To make of pieces or patches; to repair as with patches; to arrange in a hasty or clumsy manner; -- generally with up; as, to patch up a truce.
n.
Way; track; path.
v. t.
To mend by sewing on a piece or pieces of cloth, leather, or the like; as, to patch a coat.
v. t.
To mend with pieces; to repair with pieces festened on; to repair clumsily; as, to patch the roof of a house.