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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)
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
In graph theory, a cycle decomposition is a decomposition (a partitioning of a graph's edges) into cycles. Every vertex in a graph that has a cycle decomposition
Cycle decomposition (graph theory)
Cycle_decomposition_(graph_theory)
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
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)
Edge that connects a node to itself
a directed graph, a loop adds one to the in degree and one to the out degree. Cycle (graph theory) Graph theory Glossary of graph theory Möbius ladder
Loop_(graph_theory)
Length of a shortest cycle contained in the graph
In graph theory, the girth of an undirected graph is the length of a shortest cycle contained in the graph. If the graph does not contain any cycles (that
Girth_(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
All even-degree subgraphs of a graph
In graph theory, a branch of mathematics, the (binary) cycle space of an undirected graph is the set of its even-degree spanning subgraphs, or the set
Cycle_space
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)
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
3-regular graph with no 3-edge-coloring
In the study of various important and difficult problems in graph theory (such as the cycle double cover conjecture and the 5-flow conjecture), one encounters
Snark_(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
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
Directed graph with no directed cycles
mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it consists
Directed_acyclic_graph
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
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
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)
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
Cycle graph plus universal vertex
In graph theory, a wheel graph is a graph formed by connecting a single universal vertex to all vertices of a cycle. A wheel graph with n vertices can
Wheel_graph
Graphs that differ only by edge subdivision
In graph theory, two graphs G {\displaystyle G} and G ′ {\displaystyle G'} are homeomorphic if there is a graph isomorphism from some subdivision of G
Homeomorphism_(graph_theory)
Unproven conjecture in graph theory
mathematics Must every cubic graph contain a simple cycle of length a power of two? More unsolved problems in mathematics In graph theory, the unproven Erdős–Gyárfás
Erdős–Gyárfás_conjecture
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)
Cycles in a graph that cover each edge twice
In graph-theoretic mathematics, a cycle double cover is a collection of cycles in an undirected graph that together include each edge of the graph exactly
Cycle_double_cover
Index of articles associated with the same name
functions Cycle decomposition (graph theory) Cycle decomposition (group theory) Cyclic extension, a field extension with cyclic Galois group Graph theory: Cyclic
Cyclic_(mathematics)
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)
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
Index of articles associated with the same name
cyclic graph may mean a graph that contains a cycle, or a graph that is a cycle, with varying definitions of cycles. See: Cycle (graph theory), a cycle in
Cyclic_graph
Binary operation combining the vertex and edge sets of two graphs
In graph theory, a branch of mathematics, the disjoint union of graphs is an operation that combines two or more graphs to form a larger graph. It is
Disjoint_union_of_graphs
Cycles in a graph that generate all cycles
In graph theory, a branch of mathematics, a cycle basis of an undirected graph is a set of simple cycles that forms a basis of the cycle space of the
Cycle_basis
Undirected graph with 14 vertices
mathematical field of graph theory, the Heawood graph is an undirected graph with 14 vertices and 21 edges, named after Percy John Heawood. The graph is cubic, and
Heawood_graph
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
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
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
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)
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 structure studied in group theory
In group theory, a subfield of abstract algebra, a cycle graph of a group is an undirected graph that illustrates the various cycles of that group, given
Cycle_graph_(algebra)
Characteristic of undirected graphs
graph theory, a branch of mathematics, the rank of an undirected graph has two unrelated definitions. Let n equal the number of vertices of the graph
Rank_(graph_theory)
Problem of finding a cycle through all vertices of a graph
theory and graph theory. It decides if a directed or undirected graph, G, contains a Hamiltonian path, a path that visits every vertex in the graph exactly
Hamiltonian_path_problem
Mathematical tree of cycles
In graph theory, a cactus (sometimes called a cactus tree) is a connected graph in which any two simple cycles have at most one vertex in common. Equivalently
Cactus_graph
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)
Graph defined from a mathematical group
point. Vertex-transitive graph Generating set of a group Lovász conjecture Cube-connected cycles Algebraic graph theory Cycle graph (algebra) Proof: Let σ
Cayley_graph
Subgraph induced by all nodes linked to a given node of a graph
In graph theory, the neighbourhood of a vertex v in a graph G is the subgraph of G induced by all the vertices that are connected to v by an edge (vertices
Neighbourhood_(graph_theory)
Graph where all long cycles have a chord
of graph theory, a chordal graph is one in which all cycles of four or more vertices have a chord, which is an edge that is not part of the cycle but
Chordal_graph
One of two types of graph
In graph theory, a book graph (often written B p {\displaystyle B_{p}} ) may be any of several kinds of graph formed by multiple cycles sharing an edge
Book_(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
of graphs contains definitions of graphs and graph families. For collected definitions of graph theory terms that do not refer to individual graph types
List_of_graphs
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)
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
4-regular undirected graph in mathematics
In the mathematical field of graph theory, the Robertson graph or (4,5)-cage, is a 4-regular undirected graph with 19 vertices and 38 edges named after
Robertson_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
Unproven generalization of the four-color theorem
complete graph as a minor? More unsolved problems in mathematics In graph theory, the Hadwiger conjecture states that if G {\displaystyle G} is loopless
Hadwiger conjecture (graph theory)
Hadwiger_conjecture_(graph_theory)
Linear algebra aspects of graph theory
In mathematics, spectral graph theory is the study of the properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors
Spectral_graph_theory
Influence of local substructure of a graph on global properties
essence, extremal graph theory studies how global properties of a graph influence local substructure. Results in extremal graph theory deal with quantitative
Extremal_graph_theory
Graph containing cycles of all possible lengths
In the mathematical study of graph theory, a pancyclic graph is a directed graph or undirected graph that contains cycles of all possible lengths from
Pancyclic_graph
Regular graph with fewest possible nodes for its girth
of graph theory, a cage is a regular graph that has as few vertices as possible for its girth. Formally, an (r, g)-graph is defined to be a graph in which
Cage_(graph_theory)
Decomposition of a graph into hamiltonion cycles
graph theory, a branch of mathematics, a Hamiltonian decomposition of a given graph is a partition of the edges of the graph into Hamiltonian cycles.
Hamiltonian_decomposition
Topics referred to by the same term
boundary Cycle (graph theory), a nontrivial path in a graph from a node to itself Cycle graph, a graph that is itself a cycle Cycle matroid, a matroid derived
Cycle
Bipartite non-Hamiltonian polyhedral graph
In graph theory, a branch of mathematics, the Herschel graph is a bipartite undirected graph with 11 vertices and 18 edges. It is a polyhedral graph (the
Herschel_graph
Graph linking pairs of comparable elements in a partial order
In graph theory and order theory, a comparability graph is an undirected graph that connects pairs of elements that are comparable to each other in a
Comparability_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
Graph without triples of adjacent vertices
area of graph theory, a triangle-free graph is an undirected graph in which no three vertices form a triangle of edges. Triangle-free graphs may be equivalently
Triangle-free_graph
Graph of chess rook moves
In graph theory, a rook's graph is an undirected graph that represents all legal moves of the rook chess piece on a chessboard. Each vertex of a rook's
Rook's_graph
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
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
Tree graph with one central node and leaves of length 1
In graph theory, the star Sk is the complete bipartite graph K1, k, that is, it is a tree with one internal node and k leaves. Alternatively, some authors
Star_(graph_theory)
Non-crossing graph with vertices on outer face
In graph theory, an outerplanar graph is a graph that has a planar drawing for which all vertices belong to the outer face of the drawing. Outerplanar
Outerplanar_graph
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
Type of graph
In graph theory, a biconnected graph is a connected and "nonseparable" graph, meaning that if any one vertex were to be removed, the graph will remain
Biconnected_graph
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
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
mathematical field of graph theory, a core is a notion that describes behavior of a graph with respect to graph homomorphisms. Graph C {\displaystyle C}
Core_(graph_theory)
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 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
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)
Graph with tight clique-coloring relation
In graph theory, a perfect graph is a graph in which the chromatic number equals the size of the maximum clique, both in the graph itself and in every
Perfect_graph
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
Connectivity measure in graph theory
In graph theory, the cycle rank of a directed graph is a digraph connectivity measure proposed first by Eggan and Büchi (Eggan 1963). Intuitively, this
Cycle_rank
Partition of a graph into spanning subgraphs
mathematics In graph theory, a factor of a graph G is a spanning subgraph, i.e., a subgraph that has the same vertex set as G. A k-factor of a graph is a spanning
Graph_factorization
Graph whose vertices correspond to combinations of a set of n elements
In graph theory, the Kneser graph K(n, k) (alternatively KGn,k) is the graph whose vertices correspond to the k-element subsets of a set of n elements
Kneser_graph
Graph of numbers differing by a square
the number theory of quadratic residues, and have interesting properties that make them useful in graph theory more generally. Paley graphs are named after
Paley_graph
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
field of graph theory, an integral graph is a graph whose adjacency matrix's spectrum consists entirely of integers. In other words, a graph is an integral
Integral_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
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)
Theorem on Hamiltonian graphs
In graph theory, a branch of mathematics, Fleischner's theorem gives a sufficient condition for a graph to contain a Hamiltonian cycle. It states that
Fleischner's_theorem
In graph theory, a branch of mathematics, an edge cycle cover (sometimes called simply cycle cover) of a graph is a family of cycles which are subgraphs
Edge_cycle_cover
Cubic graph with 28 vertices and 42 edges
field of graph theory, the Coxeter graph is a 3-regular graph with 28 vertices and 42 edges. It is one of the 13 known cubic distance-regular graphs. It is
Coxeter_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)
Graph of short distances in another graph
In graph theory, a branch of mathematics, the kth power Gk of an undirected graph G is another graph that has the same set of vertices, but in which two
Graph_power
On graph coloring and neighborhood size
In graph theory, Brooks' theorem states a relationship between the maximum degree of a graph and its chromatic number. According to the theorem, in a
Brooks'_theorem
Mathematical tree with cycle through leaves
In graph theory, a Halin graph is a type of planar graph, constructed by connecting the leaves of a tree into a cycle. The tree must have at least four
Halin_graph
Cubic graph with 8 vertices and 12 edges
mathematical field of graph theory, the Wagner graph is a 3-regular graph with 8 vertices and 12 edges. It is the 8-vertex Möbius ladder graph. As a Möbius ladder
Wagner_graph
Undirected graph acted on by a vertex-transitive cyclic group of symmetries
In graph theory, a circulant graph is an undirected graph acted on by a cyclic group of symmetries which takes any vertex to any other vertex. It is sometimes
Circulant_graph
Gluing graphs at complete subgraphs
In graph theory, a branch of mathematics, a clique sum (or clique-sum) is a way of combining two graphs by gluing them together at a clique, analogous
Clique-sum
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
Topics referred to by the same term
complexity Circuit complexity, a branch of computational complexity theory Cycle (graph theory), a closed path, with no other repeated vertices than the starting
Circuit
Graph in which all ordered pairs of linked nodes are automorphic
In the mathematical field of graph theory, a graph G is symmetric or arc-transitive if, given any two ordered pairs of adjacent vertices ( u 1 , v 1 )
Symmetric_graph
On existence of a strongly regular graph
exist a strongly regular graph with parameters (99,14,1,2)? More unsolved problems in mathematics In graph theory, Conway's 99-graph problem is an unsolved
Conway's_99-graph_problem
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
CYCLE GRAPH-THEORY
CYCLE GRAPH-THEORY
Boy/Male
Hebrew, Hindu, Indian, Marathi
Grape Cluster
Girl/Female
Muslim
Grape like
Boy/Male
Biblical
A grape, a knot.
Boy/Male
Tamil
Jaramarana Varjita | ஜராமாஂரநா வரà¯à®œà¯€à®¤à®¾
Free from the cycle of births and deaths
Jaramarana Varjita | ஜராமாஂரநா வரà¯à®œà¯€à®¤à®¾
Girl/Female
Indian
Grape like
Girl/Female
Indian
Grape vine
Boy/Male
African, Arabic
Grape Vines
Girl/Female
Muslim
Grape vine
Girl/Female
Tamil
Kaslunira | கஸà¯à®²à¯à®‚நீரா
Grape, Belonging to kashmir
Kaslunira | கஸà¯à®²à¯à®‚நீரா
Biblical
a grape; a knot
Girl/Female
Arabic, Assamese, Hindu, Indian, Kannada, Malayalam, Marathi, Muslim, Telugu
Grape
Girl/Female
Hindu, Indian, Traditional
The Periphery or Rim of a Wheel or Cycle
Boy/Male
Afghan, Hebrew, Indian, Parsi, Sanskrit
Grape Presser; World; Song
Boy/Male
Biblical
A grape, a knot.
Boy/Male
Hindu
Free from the cycle of births and deaths
Boy/Male
Muslim
Grape
Girl/Female
Hindu
Grape, Belonging to kashmir
Boy/Male
Arabic, Modern
Grape
Boy/Male
Indian
Grape
Boy/Male
Hindu, Indian, Punjabi, Sikh
From Kashmir; Grape
CYCLE GRAPH-THEORY
CYCLE GRAPH-THEORY
CYCLE GRAPH-THEORY
CYCLE GRAPH-THEORY
CYCLE GRAPH-THEORY
CYCLE GRAPH-THEORY
CYCLE GRAPH-THEORY