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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
Isomorphism of an object to itself
nontrivial automorphism: negation. Considered as a ring, however, it has only the trivial automorphism. Generally speaking, negation is an automorphism of any
Automorphism
Graph in which all ordered pairs of linked nodes are automorphic
v 2 . {\displaystyle f(v_{1})=v_{2}.} In other words, a graph is symmetric if its automorphism group acts transitively on ordered pairs of adjacent vertices
Symmetric_graph
Graph where any two nodes of equal distance are isomorphic
distance-transitive graph is interesting partly because it has a large automorphism group. Some interesting finite groups are the automorphism groups of distance-transitive
Distance-transitive_graph
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
k-ultrahomogeneous graph is a graph in which every isomorphism between two of its induced subgraphs of at most k vertices can be extended to an automorphism of the
Homogeneous_graph
Bijection between the vertex set of two graphs
a mapping of a graph onto itself, i.e., when G and H are one and the same graph, the isomorphism is called an automorphism of G. Graph isomorphism is
Graph_isomorphism
"field automorphisms" (generated by a Frobenius automorphism), and g is the order of the group of "graph automorphisms" (coming from automorphisms of the
List_of_finite_simple_groups
Undirected graph with no non-trivial symmetries
identity mapping of a graph is always an automorphism, and is called the trivial automorphism of the graph. An asymmetric graph is a graph for which there are
Asymmetric_graph
Mathematical group
In mathematics, the outer automorphism group of a group, G, is the quotient, Aut(G) / Inn(G), where Aut(G) is the automorphism group of G and Inn(G) is
Outer_automorphism_group
Graph defined from a mathematical group
{\displaystyle \sigma :V(\Gamma )\to V(\Gamma )} be an arbitrary automorphism of the colored directed graph Γ {\displaystyle \Gamma } , and let h = σ ( e ) {\displaystyle
Cayley_graph
alternating path; see alternating. automorphism A graph automorphism is a symmetry of a graph, an isomorphism from the graph to itself. bag One of the sets
Glossary_of_graph_theory
Cubic graph with 10 vertices and 15 edges
graph can be transformed into every other such path by a symmetry of the graph. It is one of only 13 cubic distance-regular graphs. The automorphism group
Petersen_graph
Distance-regular graph with 56 vertices
neighborhood of any vertex in the Gosset graph is isomorphic to the Schläfli graph. The automorphism group of the Gosset graph is isomorphic to the Coxeter group
Gosset_graph
Unsolved problem in computational complexity theory
problems. Finding a graph's automorphism group. Counting automorphisms of a graph. The recognition of self-complementarity of a graph or digraph. A clique
Graph_isomorphism_problem
Cubic graph with 12 vertices and 18 edges
vertex is 3. It is one of the five smallest cubic graphs possessing only a single graph automorphism, the identity: every vertex can be distinguished topologically
Frucht_graph
Graph property
distance-transitive graphs, having the numerical regularity properties of the latter without necessarily having a large automorphism group. The intersection
Distance-regular_graph
Brouwer–Haemers graph Local McLaughlin graph Perkel graph Gewirtz graph A symmetric graph is one in which there is a symmetry (graph automorphism) taking any
List_of_graphs
Graph of chess rook moves
be extended to an automorphism of the whole graph. A rook's graph can also be viewed as the line graph of a complete bipartite graph Kn,m — that is, it
Rook's_graph
Vertices connected in pairs by edges
graphs with large automorphism groups: vertex-transitive, arc-transitive, and distance-transitive graphs; strongly regular graphs and their generalizations
Graph_(discrete_mathematics)
degree 22. Thus all 100 vertices have degree 22 each. The automorphism group of the Higman–Sims graph is a group of order 88,704,000 isomorphic to the semidirect
Higman–Sims_graph
Graph with all vertices of degree 3
the five smallest cubic graphs without any symmetries: it possesses only a single graph automorphism, the identity automorphism. According to Brooks' theorem
Cubic_graph
Area of discrete mathematics
particularly automorphism groups and geometric group theory, focuses on various families of graphs based on symmetry in algebraic graph theory. Such a
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
Planar graph with 5 nodes and 6 edges
mathematical field of graph theory, the butterfly graph (also called the bowtie graph and the hourglass graph) is a planar, undirected graph with 5 vertices
Butterfly_graph
One of two different regular graphs with 16 vertices
polynomial, making it a graph determined by its spectrum. The 5-regular Clebsch graph is a Cayley graph with an automorphism group of order 1920, isomorphic
Clebsch_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
Undirected graph named after S. S. Shrikhande
The automorphism group of the Shrikhande graph is of order 192. It acts transitively on the vertices, on the edges and on the arcs of the graph. Therefore
Shrikhande_graph
Undirected graph with 14 vertices
and no vertex embedded into a point within an edge. The automorphism group of the Heawood graph is isomorphic to the projective linear group PGL2(7), a
Heawood_graph
rounded up. This graph is not vertex-transitive: its automorphism group has one orbit on vertices of size 8, and one of size 4. The Chvátal graph is Hamiltonian
Chvátal_graph
In graph-theoretic mathematics, a biregular graph or semiregular bipartite graph is a bipartite graph G = ( U , V , E ) {\displaystyle G=(U,V,E)} for which
Biregular_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
Connectivity_(graph_theory)
Generalization of graph theory
definition of equality, graphs are self-dual: ( H ∗ ) ∗ = H {\displaystyle \left(H^{*}\right)^{*}=H} A hypergraph automorphism is an isomorphism from a
Hypergraph
Type of graph in graph theory
; Yellen, J. (2004). Handbook of Graph Theory. CRC Press. p. 491. ISBN 1-58488-090-2. Babai, L (1996). "Automorphism groups, isomorphism, reconstruction"
Half-transitive_graph
3-regular graph with 30 vertices and 45 edges
to five edges in the Tutte–Coxeter graph is equivalent to any other such path by one such automorphism. This graph is the spherical building associated
Tutte–Coxeter_graph
by an automorphism, that is, an isomorphism of the object to itself. This idea applies also to graphs. For example, consider the simple graph G {\displaystyle
Fibration_symmetry
Branch of mathematics
second branch of algebraic graph theory involves the study of graphs in connection to group theory, particularly automorphism groups and geometric group
Algebraic_graph_theory
Cubic graph with 8 vertices and 12 edges
same number of vertices. The Wagner graph is a vertex-transitive graph but is not edge-transitive. Its full automorphism group is isomorphic to the dihedral
Wagner_graph
vertices. The automorphism group of the Tutte graph is Z/3Z, the cyclic group of order 3. The characteristic polynomial of the Tutte graph is : ( x − 3
Tutte_graph
Class of undirected graphs defined from systems of sets
Bibcode:2008arXiv0811.2981R. Ramras, Mark; Donovan, Elizabeth (2011), "The automorphism group of a Johnson graph", SIAM Journal on Discrete Mathematics, 25 (1): 267–270
Johnson_graph
Cubic graph with 28 vertices and 42 edges
independent set including v, leaving behind the Coxeter graph. The automorphism group of the Coxeter graph is a group of order 336. It acts transitively on the
Coxeter_graph
graph. The group theorist Jack McLaughlin discovered that the automorphism group of this graph had a subgroup of index 2 which was a previously undiscovered
McLaughlin_graph
7-regular undirected graph with 50 nodes and 175 edges
Hoffman-Singleton graph. It should instead be ( − 1 ) a b y {\displaystyle (-1)^{a}by} as written here.) The automorphism group of the Hoffman–Singleton graph is a
Hoffman–Singleton_graph
4-vertex-connected and a 4-edge-connected graph. It has book thickness 3 and queue number 3. The graph is not 1-planar. It has an automorphism group of order 54. This is
Holt_graph
Two special graphs in graph theory
bipartite. It can be derived from the 28-vertex Coxeter graph. The automorphism group of the Klein graph is the group PGL2(7) of order 336, which has PSL2(7)
Klein_graphs
Bipartite non-Hamiltonian polyhedral graph
faces are nine quadrilaterals. This can be designed so that each graph automorphism corresponds to a symmetry of the polyhedron, in which case three of
Herschel_graph
Infinite graph containing all countable graphs
to an automorphism of the whole graph is expressed by saying that the Rado graph is ultrahomogeneous. In particular, there is an automorphism taking
Rado_graph
Planar graph with 4 nodes and 5 edges
forbidden minors, the family of graphs obtained is the family of pseudoforests. The full automorphism group of the diamond graph is a group of order 4 isomorphic
Diamond_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 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
Bipartite, 3-regular undirected graph
The automorphism group of the Pappus graph is a group of order 216. It acts transitively on the vertices, on the edges and on the arcs of the graph. Therefore
Pappus_graph
Triangle-free graph requiring four colors
graph is the smallest triangle-free graph with its chromatic number. The full automorphism group of the Grötzsch graph is isomorphic to the dihedral group
Grötzsch_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
Graph where all pairs of edges are automorphic
mathematical 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
Edge-transitive_graph
Aspect of mathematical group theory
precisely the outer automorphism of S6. Being an automorphism, the map must preserve the order of elements, but unlike inner automorphisms, it does not preserve
Automorphisms of the symmetric and alternating groups
Automorphisms_of_the_symmetric_and_alternating_groups
The Suzuki graph is a strongly regular graph with parameters ( 1782 , 416 , 100 , 96 ) {\displaystyle (1782,416,100,96)} . Its automorphism group has order
Suzuki_graph
Methodic assignment of colors to elements of a graph
coloring of a graph is an orbit of a coloring under the action of the automorphism group of the graph. The colors remain labeled; it is the graph that is unlabeled
Graph_coloring
16-regular graph with 27 vertices and 216 edges
to an automorphism of the whole graph. If a graph is 5-ultrahomogeneous, it is ultrahomogeneous for every k; the only finite connected graphs of this
Schläfli_graph
On graphs with given symmetry groups
that the automorphism group of each of them is isomorphic to G {\displaystyle G} . The main idea of the proof is to observe that the Cayley graph of G, with
Frucht's_theorem
in graphs. IV. Linear arboricity". Networks. 11 (1): 69–72. doi:10.1002/net.3230110108. MR 0608921.. Babai, László (June 9, 1994). "Automorphism groups
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Undirected cubic graph with 12 vertices and 18 edges
NP-complete. Tietze's graph has chromatic number 3, chromatic index 4, girth 3 and diameter 3. The independence number is 5. Its automorphism group has order
Tietze's_graph
Fortnow has written a concise proof of this theorem. ⊕P contains the graph automorphism problem, and in fact this problem is low for ⊕P. It also trivially
Parity_P
Pictorial representation of symmetry
D4, there is a single non-trivial automorphism (Out = C2, the cyclic group of order 2), while for D4, the automorphism group is the symmetric group on three
Dynkin_diagram
Every graph has evenly many odd vertices
In graph theory, the handshaking lemma is the statement that, in every finite undirected graph, the number of vertices that touch an odd number of edges
Handshaking_lemma
Strongly regular graph
parameters (77,16,0,4). The automorphism group is of order 887040 and is isomorphic to the stabilizer of a point in the automorphism group of NL2(10)" Slide
M22_graph
Geometry with 7 points and 7 lines
The automorphism group GL(3, 2) of the group (Z2)3 is that of the Fano plane, and has order 168. As with any incidence structure, the Levi graph of the
Fano_plane
Graph that is edge-transitive and regular but not vertex-transitive
symmetry maps the first into the second. A semi-symmetric graph must be bipartite, and its automorphism group must act transitively on each of the two vertex
Semi-symmetric_graph
Natural number
In graph theory, all graphs with four or fewer vertices are planar, however, there is a graph with five vertices that is not: K5, the complete graph with
5
Tree graph with one central node and leaves of length 1
star has large automorphism group, namely, the symmetric group on k letters. Stars may also be described as the only connected graphs in which at most
Star_(graph_theory)
′ {\displaystyle w'} . A Whitehead automorphism, or Whitehead move, of F n {\displaystyle F_{n}} is an automorphism τ ∈ Aut ( F n ) {\displaystyle \tau
Whitehead's_algorithm
Index of articles associated with the same name
illustrates the cyclic subgroups of a group Circulant graph, a graph with an automorphism which permutes its vertices cyclically. This set index article
Cyclic_graph
Robertson graph is one of the smallest graphs with cop number 4. The Robertson graph is not a vertex-transitive graph; its full automorphism group is isomorphic
Robertson_graph
Graph where each vertex has the same number of neighbors
In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency. A regular
Regular_graph
Solid with 12 equal pentagonal faces
replicated in the properties of this graph, which are distance-transitive, distance-regular, and symmetric. The automorphism group has order a hundred and twenty
Regular_dodecahedron
Positive-definite integral set of repeated points with Abelian group-rank 24
lattice. G0×G1×G2 is the order of the automorphism group of the lattice G∞×G1×G2 is the order of the automorphism group of the corresponding deep hole
Niemeier_lattice
Planar bipartite graph with 25 vertices and 31 edges
polyhedral graphs. The Walther graph is an identity graph; its automorphism group is the trivial group. The characteristic polynomial of the Walther graph is :
Walther_graph
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
Graph with a triangular truncated trapezohedron as its skeleton
Thus, it is a planar unit-distance graph that is not a matchstick graph. The automorphism group both of the Dürer graph and of the Dürer solid (in either
Dürer_graph
Graph with same nodes as but complementary connections to another
The automorphism group of a graph is the automorphism group of its complement. The complement of every triangle-free graph is a claw-free graph, but
Complement_graph
Graph made from disjoint union of complete graphs
to an automorphism of the whole graph. With only two exceptions, the cluster graphs and their complements are the only finite homogeneous graphs, and infinite
Cluster_graph
regular two-graphs, strongly regular graphs, and also finite groups because many regular two-graphs have interesting automorphism groups. A two-graph is not
Two-graph
Topics referred to by the same term
wireless telephony Gimp Animation Package, an extension for the GIMP Graph automorphism problem Gap (chart pattern), areas where no trading occurs in the
Gap
Mathematical tree with cycle through leaves
The Frucht graph, one of the five smallest cubic graphs with no nontrivial graph automorphisms, is also a Halin graph. Every Halin graph is 3-connected
Halin_graph
Undirected bipartite graph with 112 vertices and 168 edges
most one point. The automorphism group of the Ljubljana graph is a group of order 168. It acts transitively on the edges the graph but not on its vertices:
Ljubljana_graph
largest distance-transitive graph with degree 11 and diameter ≤ 4.[citation needed] The automorphism group of the Livingstone graph is the sporadic simple
Livingstone_graph
Complexity class of problems
designated sink vertex. Graph isomorphism problem Finding a graph's automorphism group Finding the number of graph automorphisms Planar minimum bisection
NP-intermediate
Outer automorphism group of a free group on n generators
outer automorphism group of the fundamental group of that surface. Given any finite graph with fundamental group F n {\displaystyle F_{n}} , the graph can
Out(Fn)
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
Symmetric bipartite cubic graph with 16 vertices and 24 edges
automorphism group of the Möbius–Kantor graph is a group of order 96. It acts transitively on the vertices, on the edges and on the arcs of the graph
Möbius–Kantor_graph
Constructs with triply-connected vertices
Estrada index and Kirchhoff index. Aut is the order of the Automorphism group of the graph. A Hamiltonian circuit (where present) is indicated by enumerating
Table_of_simple_cubic_graphs
Regular graph with girth more than twice its diameter
in graph theory. Although all the known Moore graphs are vertex-transitive graphs, any of degree 57 cannot be vertex-transitive, as its automorphism group
Moore_graph
Undirected graph acted on by a vertex-transitive cyclic group of symmetries
cyclic graph, but this term has other meanings. Circulant graphs can be described in several equivalent ways: The automorphism group of the graph includes
Circulant_graph
3-edge-connected graph. It has book thickness 3 and queue number 2. The graph is 1-planar. The automorphism group of the Dyck graph is a group of order
Dyck_graph
Graph structure studied in group theory
{\displaystyle C_{2}} maps to the multiply-by-5 automorphism of C 8 {\displaystyle C_{8}} . In drawing the cycle graphs of those two groups, we take C 8 × C 2
Cycle_graph_(algebra)
24-vertex symmetric bipartite cubic graph
state-transition graph is the Nauru graph. In other words, it is the arrangement graph A 4 , 3 {\displaystyle A_{4,3}} . The automorphism group of the Nauru graph is
Nauru_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
Bipartite graph where each node of 1st set is linked to all nodes of 2nd set
In the mathematical field of graph theory, a complete bipartite graph or biclique is a special kind of bipartite graph where every vertex of the first
Complete_bipartite_graph
Graph often embedded in the Klein bottle
3-vertex-connected and 3-edge-connected perfect graph. The automorphism group of the Franklin graph is of order 48 and is isomorphic to Z/2Z×S4, the
Franklin_graph
making it a semi-symmetric graph, a regular graph that is edge-transitive but not vertex-transitive. In fact, the automorphism group of the Tutte 12-cage
Tutte_12-cage
3-edge-connected graph. The graph is 1-planar. The F26A graph is Hamiltonian and can be described by the LCF notation [−7, 7]13. The automorphism group of the
F26A_graph
GRAPH AUTOMORPHISM
GRAPH AUTOMORPHISM
Girl/Female
Tamil
Kaslunira | கஸà¯à®²à¯à®‚நீரா
Grape, Belonging to kashmir
Kaslunira | கஸà¯à®²à¯à®‚நீரா
Boy/Male
Biblical
A grape, a knot.
Female
Thai/Siamese
Thai name A-GUN means "grape."
Girl/Female
Afghan, Arabic, Hebrew, Indian, Muslim, Parsi, Sanskrit
Grape Presser; World; Song; Universe
Boy/Male
Hebrew, Hindu, Indian, Marathi
Grape Cluster
Boy/Male
Afghan, Hebrew, Indian, Parsi, Sanskrit
Grape Presser; World; Song
Girl/Female
Indian
Grape like
Girl/Female
Arabic, Assamese, Hindu, Indian, Kannada, Malayalam, Marathi, Muslim, Telugu
Grape
Boy/Male
Biblical
A grape, a knot.
Boy/Male
African, Arabic
Grape Vines
Boy/Male
Hindu, Indian, Punjabi, Sikh
From Kashmir; Grape
Girl/Female
Hindu
Grape, Belonging to kashmir
Girl/Female
Muslim
Grape like
Biblical
a grape; a knot
Girl/Female
Indian
Grape vine
Boy/Male
Hindu, Indian
Efficient; Conqueror of Miseries; Bond in Affection; Capable; Mysterious; Different than Others; Smart; Most Mysterious Vastu Grah 'Rahu'; Son of Lord Buddha; Son of Goddess Durga; Truth Follower; Best of All
Boy/Male
Indian
Grape
Girl/Female
Muslim
Grape vine
Boy/Male
Arabic, Modern
Grape
Boy/Male
Muslim
Grape
GRAPH AUTOMORPHISM
GRAPH AUTOMORPHISM
Girl/Female
American, Australian, British, Chinese, Christian, Dutch, English, French, German, Indian, Jamaican, Latin, Swedish
Longed for; Desired; Longing
Boy/Male
English
Watercress river.
Male
English
English form of Latin Valentinus, VALENTINE means "healthy, strong." Compare with feminine Valentine.
Boy/Male
German, Spanish
Lion-bold; Lion
Boy/Male
Indian, Punjabi, Sikh
Glorious Victory
Boy/Male
Indian, Punjabi, Sikh
Sweet
Boy/Male
Indian
Person who makes sacrifice
Girl/Female
Indian
Walking with proud, Swinging gait, Pretty
Girl/Female
Tamil
A musical instrument, The melodious voice of the cuckoo, Chirping of birds
Girl/Female
Hindu, Indian
Being First
GRAPH AUTOMORPHISM
GRAPH AUTOMORPHISM
GRAPH AUTOMORPHISM
GRAPH AUTOMORPHISM
GRAPH AUTOMORPHISM
n.
Grapeshot.
n.
The cultivation of the vine; grape growing.
n.
A grape, or a bunch of grapes.
n.
A mangy tumor on the leg of a horse.
n.
A grape dried in the sun; a raisin.
a.
Composed of, or resembling, grapes.
n.
A variety of shaddock, called also grape fruit.
n.
A sort of grape.
n.
The plant which bears this fruit; the grapevine.
a.
Full of small kernels like a grape.
n.
A plant of the genus Muscari; grape hyacinth.
n.
A white grape, esteemed for the table.
n.
The Hartford grape, a variety of grape first raised at Hartford, Connecticut, from the Northern fox grape. Its large dark-colored berries ripen earlier than those of most other kinds.
a.
Resembling a grape.
n.
See Grasshopper, and Frog hopper, Grape hopper, Leaf hopper, Tree hopper, under Frog, Grape, Leaf, and Tree.
n.
A well-known edible berry growing in pendent clusters or bunches on the grapevine. The berries are smooth-skinned, have a juicy pulp, and are cultivated in great quantities for table use and for making wine and raisins.
n.
A seed of the grape.
n.
A grape of many varieties and colors.