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Symmetric tessellation of a closed surface
and Galois theory. Regular maps are classified according to either: the genus and orientability of the supporting surface, the underlying graph, or the automorphism
Regular_map_(graph_theory)
Topics referred to by the same term
polynomial function of algebraic varieties a regular map (graph theory), a symmetric 2-cell embedding of a graph into a closed surface This disambiguation
Regular_map
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 property
In the mathematical field of graph theory, a distance-regular graph is a regular graph such that for any two vertices v and w, the number of vertices
Distance-regular_graph
Topics referred to by the same term
large graphs Regular language, a formal language recognizable by a finite state automaton (related to the regular expression) Regular map (graph theory),
Regular
Graph where all pairs of vertices are automorphic
of graph theory, an automorphism is a permutation of the vertices such that edges are mapped to edges and non-edges are mapped to non-edges. A graph is
Vertex-transitive_graph
Embedding a graph in a topological space, often Euclidean
In topological graph theory, an embedding (also spelled imbedding) of a graph G {\displaystyle G} on a surface Σ {\displaystyle \Sigma } is a representation
Graph_embedding
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)
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
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
Undirected graph named after S. S. Shrikhande
mathematical field of graph theory, the Shrikhande graph is a graph discovered by S. S. Shrikhande in 1959. It is a strongly regular graph with 16 vertices
Shrikhande_graph
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
Two special graphs in graph theory
In the mathematical field of graph theory, the Klein graphs are two different but related regular graphs, each with 84 edges. Each can be embedded in
Klein_graphs
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
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
Graph in which all ordered pairs of linked nodes are automorphic
none for t ≥ 6. Algebraic graph theory Gallery of named graphs Regular map Biggs, Norman (1993). Algebraic Graph Theory (2nd ed.). Cambridge: Cambridge
Symmetric_graph
Solid with eight equal triangular faces
edges of a regular octahedron give rise to a graph, a discrete structure drawn in a plane. The name is octahedral graph. The octahedral graph is an example
Regular_octahedron
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
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)
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 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
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
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
Function, homomorphism, or morphism
are also a few less common uses in logic and graph theory. In many branches of mathematics, the term map is used to mean a function, sometimes with a
Map_(mathematics)
Type of continuous map in topology
lattice is the universal cover of a Cayley graph Covering graph, a covering space for an undirected graph, and its special case the bipartite double cover
Covering_space
Graph related to another graph by a covering map
the mathematical discipline of graph theory, a graph C is a covering graph of another graph G if there is a covering map from the vertex set of C to the
Covering_graph
7-regular undirected graph with 50 nodes and 175 edges
of graph theory, the Hoffman–Singleton graph is a 7-regular undirected graph with 50 vertices and 175 edges. It is the unique strongly regular graph with
Hoffman–Singleton_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
Solid with twenty equal triangular faces
icosahedral graph represents the skeleton of a regular icosahedron. Many polyhedra and other related figures are constructed from the regular icosahedron
Regular_icosahedron
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
Planar maps require at most four colors
coloring of maps can also be stated in terms of graph theory, by considering it in terms of constructing a graph coloring of the planar graph of adjacencies
Four_color_theorem
Trees with additional directed half edges
planar graphs, blossom trees are trees with additional directed half edges. Each blossom tree is associated with an embedding of a planar graph. Blossom
Blossom_tree_(graph_theory)
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
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
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
Unsolved problem in computational complexity theory
bipartite Eulerian graphs bipartite regular graphs line graphs split graphs chordal graphs regular self-complementary graphs polytopal graphs of general, simple
Graph_isomorphism_problem
of graph theory, the sphericity of a graph is a graph invariant defined to be the smallest dimension of Euclidean space required to realize the graph as
Sphericity_(graph_theory)
Combinatorial representation of a graph on an orientable surface
A combinatorial map is a combinatorial representation of a graph on an orientable surface. A combinatorial map may also be called a combinatorial embedding
Combinatorial_map
spectral graph theory, distributed computing, symbolic dynamics, graph neural networks, and category theory, under different names such as graph divisor
Fibrations_of_graphs
Distance-transitive cubic graph with 20 nodes and 30 edges
In the mathematical field of graph theory, the Desargues graph is a distance-transitive, cubic graph with 20 vertices and 30 edges. It is named after
Desargues_graph
Graph often embedded in the Klein bottle
mathematical field of graph theory, the Franklin graph is a 3-regular graph with 12 vertices and 18 edges. The Franklin graph is named after Philip Franklin
Franklin_graph
GDSs considers finite graphs and finite state spaces. As such, the research typically involves techniques from, e.g., graph theory, combinatorics, algebra
Graph_dynamical_system
Undirected cubic graph with 12 vertices and 18 edges
In the mathematical field of graph theory, Tietze's graph is an undirected cubic graph with 12 vertices and 18 edges. It is named after Heinrich Franz
Tietze's_graph
(Schläfli–Hess)) Tessellation Tilings of regular polygons Convex uniform honeycomb Regular map (graph theory) (up to identity and idempotency) In a classification
List_of_regular_polytopes
Solid with six equal square faces
the regular octahedron, is constructed by the direct sum of three line segments. The cube can be drawn into a graph, a structure in graph theory consisting
Cube
Symmetric bipartite cubic graph with 16 vertices and 24 edges
In the mathematical field of graph theory, the Möbius–Kantor graph is a symmetric bipartite cubic graph with 16 vertices and 24 edges named after August
Möbius–Kantor_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
Operation combining two oriented knots
the knot by its regular projection by recording a simple over/under information at these crossings. In graph theory terms, a regular projection of a knot
Knot_(mathematics)
On coloring the edges of graphs
In graph theory, Vizing's theorem states that every simple undirected graph may be edge colored using a number of colors that is at most one larger than
Vizing's_theorem
Graph that is edge-transitive and regular but not vertex-transitive
graph theory, a semi-symmetric graph is an undirected graph that is edge-transitive and regular, but not vertex-transitive. In other words, a graph is
Semi-symmetric_graph
Mapping a graph onto itself without changing edge-vertex connectivity
In the mathematical field of graph theory, an automorphism of a graph is a form of symmetry in which the graph is mapped onto itself while preserving
Graph_automorphism
game Acyclic pebble game One-player pebble game Token on acyclic directed graph games: Quantified boolean formulas First-order logic of equality Provability
List of PSPACE-complete problems
List_of_PSPACE-complete_problems
Graph with 24 vertices and 36 edges
mathematical field of graph theory, the McGee graph or the (3-7)-cage is a 3-regular graph with 24 vertices and 36 edges. The McGee graph is the unique (3
McGee_graph
In the mathematical field of graph theory, the Dyck graph is a 3-regular graph with 32 vertices and 48 edges, named after Walther von Dyck. It is Hamiltonian
Dyck_graph
Natural number
prime number. The four-color theorem states that a planar graph (or, equivalently, a flat map of two-dimensional regions such as countries) can be colored
4
Type of topological space
cellulation. A loopless graph is represented by a regular 1-dimensional CW-complex. A closed 2-cell graph embedding on a surface is a regular 2-dimensional CW-complex
CW_complex
Study of optimal transportation and allocation of resources
In mathematics and economics, transportation theory or transport theory is a name given to the study of optimal transportation and allocation of resources
Transportation theory (mathematics)
Transportation_theory_(mathematics)
Periodic spatial graph
nearest each vertex of the graph are congruent 17-sided polyhedra that tile space. Its edges lie on diagonals of the regular skew polyhedron, a surface
Laves_graph
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
Planar maps require at most five colors
five color theorem is a result from graph theory that given a plane separated into regions, such as a political map of the countries of the world, the
Five_color_theorem
Graphical representation of data
diagram or graph, that organizes and represents a set of numerical or qualitative data. Maps that are adorned with extra information (map surround) for
Chart
Argentine-born American mathematician
and a researcher in algebraic topology, differential topology, graph theory, coding theory and combinatorial designs. He obtained a Licentiate degree in
Italo_Jose_Dejter
In the mathematical field of graph theory, the F26A graph is a symmetric bipartite cubic graph with 26 vertices and 39 edges. It has chromatic number 2
F26A_graph
Number of planar subgraphs to cover a graph
In graph theory, the thickness of a graph G is the minimum number of planar graphs into which the edges of G can be partitioned. That is, if there exists
Thickness_(graph_theory)
label that would lead back to v {\displaystyle v} . For a D-regular graph G, the rotation map R o t G : [ N ] × [ D ] → [ N ] × [ D ] {\displaystyle \mathrm
Rotation_map
Problem in network theory
other kinds of embeddings Book thickness Graph thickness Doubly connected edge list Regular map (graph theory) Fáry's theorem Node2vec Statistical relational
Link_prediction
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
the whole graph that maps one subgraph to the other (but does not necessarily extend the given isomorphism). A homogeneous graph is a graph that is k-homogeneous
Homogeneous_graph
Form of data structure
A scene graph is a hierarchical data structure commonly used by vector-based graphics editing applications and modern computer games, which cascades the
Scene_graph
In graph theory, circular coloring is a kind of coloring that may be viewed as a refinement of the usual graph coloring. The circular chromatic number
Circular_coloring
Branch of geometry that studies combinatorial properties and constructive methods
optimization, digital geometry, discrete differential geometry, geometric graph theory, toric geometry, and combinatorial topology. Polyhedra and tessellations
Discrete_geometry
Overview of and topical guide to algorithms
matching Hopcroft–Karp algorithm Blossom algorithm Graph coloring Clique problem Independent set (graph theory) Hamiltonian path problem Travelling salesman
Outline_of_algorithms
6 operations in topological graph theory
In topological graph theory, the Wilson operations are a group of six transformations on graph embeddings. They are generated by two involutions on embeddings
Wilson_operation
Binary operation in graph theory
In graph theory, the zig-zag product of regular graphs G , H {\displaystyle G,H} , denoted by G ∘ H {\displaystyle G\circ H} , is a binary operation which
Zig-zag_product
Mathematical problem
are the same color? More unsolved problems in mathematics In geometric graph theory, the Hadwiger–Nelson problem, named after Hugo Hadwiger and Edward Nelson
Hadwiger–Nelson_problem
Generalization of graph theory
hypergraph is a generalization of a graph in which an edge can join any number of vertices. In contrast, in an ordinary graph, an edge connects exactly two
Hypergraph
Database using graph structures for queries
the decade, cloud-based graph databases such as Amazon Neptune and Neo4j AuraDB became available. Based on graph theory, graph databases store data in
Graph_database
Set that intersects every one of a family of sets
semigroup is a regular semigroup. g {\displaystyle g} acts as a (not necessarily unique) quasi-inverse for f; within semigroup theory this is simply called
Transversal_(combinatorics)
Theorem in graph theory
In graph theory, the graph removal lemma states that when a graph contains few copies of a given subgraph, then all of the copies can be eliminated by
Graph_removal_lemma
Bipartite, 3-regular undirected graph
field of graph theory, the Pappus graph is a bipartite, 3-regular, undirected graph with 18 vertices and 27 edges, formed as the Levi graph of the Pappus
Pappus_graph
Part of the mathematical subject of group theory
fundamental group of a graph of groups. Bass–Serre theory can be regarded as one-dimensional version of the orbifold theory. Bass–Serre theory was developed by
Bass–Serre_theory
Theorem in graph theory
mathematical discipline of graph theory, the 2-factor theorem, discovered by Julius Petersen, is one of the earliest works in graph theory. It can be stated as
2-factor_theorem
Form taken by the network of interconnections of a circuit
of graph theory. Standard graph theory can be extended to deal with active components and multi-terminal devices such as integrated circuits. Graphs can
Circuit_topology_(electrical)
Simple polynomial map exhibiting chaotic behavior
can take negative values. A graph of the map can also be used to learn much about its behavior. The graph of the logistic map x n + 1 = r x ( 1 − x n )
Logistic_map
Bipartite 4-regular graph with 20 nodes and 40 edges
mathematical field of graph theory, the Folkman graph is a 4-regular graph with 20 vertices and 40 edges. It is a regular bipartite graph with symmetries taking
Folkman_graph
Embedding a graph in 3D space with no cycles interlinked
In topological graph theory, a mathematical discipline, a linkless embedding of an undirected graph is an embedding of the graph into three-dimensional
Linkless_embedding
Mathematics of smooth surfaces
visually intuitive, as it essentially says that a regular surface is a subset of ℝ3 which is locally the graph of a smooth function (whether over a region in
Differential geometry of surfaces
Differential_geometry_of_surfaces
Concerned with the notion of stability in model theory
The theory of any nowhere dense graph class. These include graph classes with bounded expansion, which in turn include planar graphs and any graph class
Stable_theory
Combinatorial approach of studying the topology of a manifold
groups. Discrete Morse theory finds its application in molecular shape analysis, skeletonization of digital images/volumes, graph reconstruction from noisy
Discrete_Morse_theory
Poset representing certain properties of a polytope
defined "regular incidence complexes" and "regular incidence polytopes". Subsequently, he and Peter McMullen developed the basics of the theory in a series
Abstract_polytope
Graph with a triangular truncated trapezohedron as its skeleton
In the mathematical field of graph theory, the Dürer graph is an undirected graph with 12 vertices and 18 edges. It is named after Albrecht Dürer, whose
Dürer_graph
Graph whose nodes are one of the vertex sets of a bipartite graph
In graph theory, the bipartite half or half-square of a bipartite graph G = (U,V,E) is a graph whose vertex set is one of the two sides of the bipartition
Bipartite_half
automata theory and control theory, branches of mathematics, theoretical computer science and systems engineering, a noncommutative signal-flow graph is a
Noncommutative signal-flow graph
Noncommutative_signal-flow_graph
Network whose degree distribution follows a power law
attract more in-links than a regular page. This generates a power-law but the resulting graph differs from the actual Web graph in other properties such as
Scale-free_network
Branch of mathematics that studies the properties of groups
In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known
Group_theory
Graph where all pairs of edges are automorphic
field of graph theory, an edge-transitive graph is a graph G such that, given any two edges e1 and e2 of G, there is an automorphism of G that maps e1 to
Edge-transitive_graph
In mathematics, a graph C*-algebra is a universal C*-algebra constructed from a directed graph. Graph C*-algebras are direct generalizations of the Cuntz
Graph_C*-algebra
Aspect of topological graph theory
In topological graph theory, the Petrie dual of an embedded graph (on a 2-manifold with all faces disks) is another embedded graph that has the Petrie
Petrie_dual
Assignment of colors to edges of a graph
In graph theory, a proper edge coloring of a graph is an assignment of "colors" to the edges of the graph so that no two incident edges have the same color
Edge_coloring
Plotting by a computer application
the shortest path on a weighted graph. Pathfinding is closely related to the shortest path problem, within graph theory, which examines how to identify
Pathfinding
REGULAR MAP-GRAPH-THEORY
REGULAR MAP-GRAPH-THEORY
Boy/Male
Muslim
Grape
Boy/Male
Gujarati, Haryanvi, Hindu, Indian, Kannada, Marathi, Telugu
Regular; Ethical; Good in Nature
Female
English
Variant spelling of English May, a pet form of Margaret, MAE means "pearl," and Mary, meaning "obstinacy, rebelliousness" or "their rebellion."
Boy/Male
Indian
Grape
Boy/Male
Arabic, Modern
Grape
Girl/Female
American, Australian, Danish, French, German, Greek, Hebrew, Japanese, Scottish, Swedish, Thai, Vietnamese
May; Goddess of Spring Growth; Brightness; Dance; Coyote; Pearl; Cherry Blossom; Apricot Blossom; Combination of Ma and Ai; Scottish Form of Margaret
Boy/Male
Hindu, Indian, Traditional
Conduct; Regular Performance of Worship
Female
Japanese
(舞) Japanese name MAI means "dance." Compare with another form of Mai.
Female
English
Short form of English Maggie, MAG means "pearl."
Boy/Male
Hindu, Indian, Tamil
Regular Winner
Male
Egyptian
, Divine Father.
Female
Vietnamese
 Vietnamese name MAI means "golden flower." Compare with another form of Mai.
Girl/Female
Hebrew
Precious.
Girl/Female
American, Anglo, Australian, British, Chinese, Christian, English, French, German, Greek, Hebrew, Japanese
The Fifth Month of the Year; Kinswomen; May; The Month May was Goddess of Spring Growth; Bitter; Pearl; Beloved
Girl/Female
Muslim
Grape like
Girl/Female
Arabic, Assamese, Hindu, Indian, Kannada, Malayalam, Marathi, Muslim, Telugu
Grape
Girl/Female
Indian
Grape vine
Girl/Female
Indian
Grape like
Girl/Female
Muslim
Grape vine
Male
English
Variant spelling of English Matt, MAT means "gift of God."
REGULAR MAP-GRAPH-THEORY
REGULAR MAP-GRAPH-THEORY
Boy/Male
Indian, Sanskrit
Initiated; Consecrated
Girl/Female
English American
From the French 'cheri' meaning darling or dear one. Also, from the white meadow.
Male
Polish
Variant spelling of Polish Fryderyk, FRYDRYK means "peaceful ruler."
Boy/Male
Indian
Mallik means great
Girl/Female
Tamil
Dayamayee | தயாமயீ
Kind, Merciful
Boy/Male
Indian
Sword that the prophet (Saw) gave to Sayyidina Ali
Boy/Male
Tamil
A flower, Rain tree
Boy/Male
Irish
Serves Saint Ruadhan.
Girl/Female
Indian
The earth
Boy/Male
Australian, British, English, Latin
Woman Dyer; Right-handed
REGULAR MAP-GRAPH-THEORY
REGULAR MAP-GRAPH-THEORY
REGULAR MAP-GRAPH-THEORY
REGULAR MAP-GRAPH-THEORY
REGULAR MAP-GRAPH-THEORY
n.
One who is not regular; especially, a soldier not in regular service.
v. t.
To cause to become regular; to regulate.
n. pl.
A division of Echini which includes the circular, or regular, sea urchins.
adv.
In a regular manner; in uniform order; methodically; in due order or time.
a.
Governed by rule or rules; steady or uniform in course, practice, or occurence; not subject to unexplained or irrational variation; returning at stated intervals; steadily pursued; orderlly; methodical; as, the regular succession of day and night; regular habits.
a.
Not regular; not conforming to a law, method, or usage recognized as the general rule; not according to common form; not conformable to nature, to the rules of moral rectitude, or to established principles; not normal; unnatural; immethodical; unsymmetrical; erratic; no straight; not uniform; as, an irregular line; an irregular figure; an irregular verse; an irregular physician; an irregular proceeding; irregular motion; irregular conduct, etc. Cf. Regular.
n.
Anything which represents graphically a succession of events, states, or acts; as, an historical map.
a.
Measured by an angle; as, angular distance.
a.
Having all the parts of the same kind alike in size and shape; as, a regular flower; a regular sea urchin.
pl.
of Regulus
a.
Of or pertaining to the jugular vein; as, the jugular foramen.
a.
Conformed to a rule; agreeable to an established rule, law, principle, or type, or to established customary forms; normal; symmetrical; as, a regular verse in poetry; a regular piece of music; a regular verb; regular practice of law or medicine; a regular building.
a.
Not regular; not bound by monastic vows or rules; not confined to a monastery, or subject to the rules of a religious community; as, a secular priest.
a.
Of or pertaining to a tile; resembling a tile, or arranged like tiles; consisting of tiles; as, a tegular pavement.
a.
Belonging to a monastic order or community; as, regular clergy, in distinction dfrom the secular clergy.
pl.
of Tegula
a.
Constituted, selected, or conducted in conformity with established usages, rules, or discipline; duly authorized; permanently organized; as, a regular meeting; a regular physican; a regular nomination; regular troops.
a.
Thorough; complete; unmitigated; as, a regular humbug.
v. t.
To represent by a map; -- often with out; as, to survey and map, or map out, a county. Hence, figuratively: To represent or indicate systematically and clearly; to sketch; to plan; as, to map, or map out, a journey; to map out business.