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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
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)
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
remaining vertices is 1. If a path graph occurs as a subgraph of another graph, it is a path in that graph. A planar graph is a graph whose vertices and edges
Graph_(discrete_mathematics)
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)
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
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
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
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)
Graph with nodes connected in a closed chain
related to Cycle graphs. Complete bipartite graph Complete graph Circulant graph Cycle graph (algebra) Null graph Path graph Some simple graph spectra. win
Cycle_graph
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
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)
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 of king moves on a chessboard
be constructed as the strong product of two path graphs. For an n × m {\displaystyle n\times m} king's graph the total number of vertices is n m {\displaystyle
King's_graph
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
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
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
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
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
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
Directed path algebra
In mathematics, a Leavitt path algebra is an algebra constructed from a directed graph. Leavitt path algebras generalize Leavitt algebras and may be considered
Leavitt_path_algebra
science, a shortest-path graph is an undirected graph defined from a set of points in the Euclidean plane. The shortest-path graph is proposed with the
Shortest-path_graph
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
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
Graph with same nodes as but complementary connections to another
self-complementary graph is a graph that is isomorphic to its own complement. Examples include the four-vertex path graph and five-vertex cycle graph. There is
Complement_graph
Basic concept of graph theory
called adjacent. A graph is said to be connected if every pair of vertices in the graph is connected. This means that there is a path between every pair
Connectivity_(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
In graph theory, a fan graph (also called a path-fan graph) is a graph formed by the join of a path graph and an empty graph on a single vertex. The fan
Fan_graph
Order-zero graph or any edgeless graph
complete graph Kn. Glossary of graph theory Cycle graph Path graph Harary, Frank; Read, Ronald C. (1974). "Is the null-graph a pointless concept?". Graphs and
Null_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
Planar, undirected graph with 2n vertices and 3n-2 edges
ladder graph is 2. Sometimes the term "ladder graph" is used for the nP2 ladder rung graph, which is the graph union of n copies of the path graph P2. The
Ladder_graph
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
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
Symmetric function invariant of graphs
function invariant of graphs studied in algebraic graph theory, a branch of mathematics. It is the weight generating function for proper graph colorings, and
Chromatic_symmetric_function
Flow graph invented by Claude Shannon
A signal-flow graph or signal-flowgraph (SFG), invented by Claude Shannon, but often called a Mason graph after Samuel Jefferson Mason who coined the
Signal-flow_graph
Franklin graph Frucht graph Goldner–Harary graph Golomb graph Grötzsch graph Harries graph Harries–Wong graph Herschel graph Hoffman graph Hofman Graph H(12
List_of_graphs
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
Path of execution between decisions
A decision-to-decision path, or DD-path, is a path of execution (usually through a flow graph representing a program, such as a flow chart) between two
Decision-to-decision_path
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
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
Partition of a graph whose components are reachable from all vertices
directed graph is called strongly connected if there is a path in each direction between each pair of vertices of the graph. That is, a path exists from
Strongly_connected_component
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)
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
Algorithm used for pathfinding and graph traversal
optimal efficiency. Given a weighted graph, a source node and a goal node, the algorithm finds the shortest path (with respect to the given weights) from
A*_search_algorithm
Graph formed by adding isolated or universal vertices
In graph theory, a threshold graph is a graph that can be constructed from a one-vertex graph by repeated applications of the following two operations:
Threshold_graph
Node labeling problem in graph theory
In graph theory, the graph bandwidth problem may be visualized as placing the vertices of a given graph at distinct integer positions along the number
Graph_bandwidth
Graph which is isomorphic to its complement
4-vertex path graph and the 5-vertex cycle graph. Every Paley graph is self-complementary. For example, the 3 × 3 rook's graph (the Paley graph of order
Self-complementary_graph
Computer science algorithm
computer science, graph traversal (also known as graph search) refers to the process of visiting (checking and/or updating) each vertex in a graph. Such traversals
Graph_traversal
discipline of graph theory, the (m,n)-tadpole graph is a special type of graph consisting of a cycle graph on m (at least 3) vertices and a path graph on n vertices
Tadpole_graph
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
Duality of graph colorings and orientations
any graph G {\displaystyle G} equals one plus the length of a longest path in an orientation of G {\displaystyle G} chosen to minimize this path's length
Gallai–Hasse–Roy–Vitaver theorem
Gallai–Hasse–Roy–Vitaver_theorem
Operation in graph theory
The Cartesian product of K2 and a path graph is a ladder graph. The Cartesian product of two path graphs is a grid graph. The Cartesian product of n edges
Cartesian_product_of_graphs
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
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
Longest distance between two vertices
vertices of the graph, and for the shortest-path distance in the graph. Diameter may be considered either for weighted or for unweighted graphs. Researchers
Diameter_(graph_theory)
One of two different regular graphs with 16 vertices
field of graph theory, the Clebsch graph is either of two complementary graphs on 16 vertices, a 5-regular graph with 40 edges and a 10-regular graph with
Clebsch_graph
Graph coloring problem on paths in a network
In graph theory, path coloring is a type of graph coloring where colors (or wavelengths) are assigned to a set of paths in a graph such that any two paths
Path_coloring
Graph of triangles with a shared vertex
the mathematical field of graph theory, the friendship graph (or Dutch windmill graph or n-fan) Fn is a planar, undirected graph with 2n + 1 vertices and
Friendship_graph
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
Binary operation in graph theory
product is the king's graph, the graph of moves of a chess king on a chessboard, which can be constructed as a strong product of path graphs. Decompositions
Strong_product_of_graphs
Graph with edges of length one, able to be drawn without crossings
In geometric graph theory, a branch of mathematics, a matchstick graph is a graph that can be drawn in the plane in such a way that its edges are line
Matchstick_graph
Describing a family of graphs by excluding certain (sub)graphs
In graph theory, a branch of mathematics, many important families of graphs can be described by a finite set of individual graphs that do not belong to
Forbidden graph characterization
Forbidden_graph_characterization
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
Graph formed from disjoint paths
In graph theory, a branch of mathematics, a linear forest is a kind of forest where each component is a path graph, or a disjoint union of nontrivial
Linear_forest
Arc-like path that the Sun appears to follow across the sky
year depict the sun path of that day. Rotterdam, the Netherlands Equator, Prime Meridian North Pole South Pole The sun path polar graphs here represent the
Sun_path
Concept in graph theory
In graph theory, a strongly regular graph (SRG) is a regular graph G = (V, E) with v vertices and degree k such that for some given integers λ , μ ≥ 0
Strongly_regular_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)
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)
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
Geometric graph with unit edge lengths
In mathematics, particularly geometric graph theory, a unit distance graph is a graph formed from a collection of points in the Euclidean plane by connecting
Unit_distance_graph
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
Directed graph isomorphic to its own transpose graph
In graph theory, a branch of mathematics, a skew-symmetric graph is a directed graph that is isomorphic to its own transpose graph, the graph formed by
Skew-symmetric_graph
{\displaystyle \chi '_{st}(G)} of the corona product of a path graph with cycle, wheel, helm and gear graphs are known. Corona products have applications in mathematical
Corona_product
Graph whose induced subgraphs preserve distance
Distance-hereditary graphs can also be characterized in several other equivalent ways: They are the graphs in which every induced path is a shortest path, or equivalently
Distance-hereditary_graph
162 papers on the subject. Removing k vertices from a path graph can split the remaining graph into as many as k + 1 connected components. The maximum
Graph_toughness
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
Node ordering for directed acyclic graphs
computer science, a topological sort or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge (u
Topological_sorting
Graph representing connectivity between cliques of another graph
four or more is a gear graph. The simplex graph of the complement graph of a path graph is a Fibonacci cube. The complete subgraphs of G can be given the
Simplex_graph
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
Mathematical game played on a graph
Graph pebbling is a mathematical game played on a graph with zero or more pebbles on each of its vertices. 'Game play' is composed of a series of pebbling
Graph_pebbling
Graph with a median for each three vertices
to shortest paths between each pair of a {\displaystyle a} , b {\displaystyle b} , and c {\displaystyle c} . The concept of median graphs has long been
Median_graph
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
Database using graph structures for queries
A graph database (GDB) is a database that uses graph structures for semantic queries with nodes, edges, and properties to represent and store data. A key
Graph_database
Algorithm for two disjoint paths in a graph
is an algorithm for finding two disjoint paths in a nonnegatively-weighted directed graph, so that both paths connect the same pair of vertices and have
Suurballe's_algorithm
Family of graphs based on the Fibonacci sequence
chemical graph theory. The Fibonacci cube may be defined in terms of Fibonacci codes and Hamming distance, independent sets of vertices in path graphs, or
Fibonacci_cube
Topics referred to by the same term
a type of junction in electronics Adobe Presenter, an Adobe software Path graph of size n {\displaystyle n} , denoted by P n {\displaystyle P_{n}} Petri
PN
NP-hard problem in combinatorial optimization
modeled as an undirected weighted graph, such that cities are the graph's vertices, paths are the graph's edges, and a path's distance is the edge's weight
Travelling_salesman_problem
Set of unordered triples from a vertex set
that are not contained in a path of T form a two-graph on the set E. A two-graph is equivalent to a switching class of graphs and also to a (signed) switching
Two-graph
Every graph has evenly many odd vertices
graph-theoretic terms as asking for an Euler path or Euler tour of a connected graph representing the city and its bridges: a walk through the graph that
Handshaking_lemma
M′. Graphs where every vertex has degree less than or equal to 2 must consist of either isolated vertices, cycles, and paths. Furthermore, each path and
Berge's_theorem
Algorithm in graph theory
or the WFI algorithm) is an algorithm for finding shortest paths in a directed weighted graph with positive or negative edge weights (but with no negative
Floyd–Warshall_algorithm
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
mathematics Is there a finite graph on at least two vertices in which each pair of distinct vertices is connected by exactly one path of length k {\displaystyle
Kotzig's_conjecture
Query language for property graphs
GQL (Graph Query Language) is a standardized query language for property graphs first described in ISO/IEC 39075, released in April 2024 by ISO/IEC. The
Graph_Query_Language
Method for finding loopless paths
In graph theory, Yen's algorithm computes single-source K-shortest loopless paths for a graph with non-negative edge cost. The algorithm was published
Yen's_algorithm
Methodic assignment of colors to elements of a graph
In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to elements of a graph. The assignment is subject to certain
Graph_coloring
Equivalence between strongly orientable graphs and bridgeless graphs
2-edge-connected graphs. That is, it is possible to choose a direction for each edge of an undirected graph G, turning it into a directed graph that has a path from
Robbins'_theorem
Method to find shortest paths
algorithm is a way to find the shortest paths between all pairs of vertices in an edge-weighted directed graph. It allows some of the edge weights to be
Johnson's_algorithm
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