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Bijection between the vertex set of two graphs
isomorphism is 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
Graph_isomorphism
Unsolved problem in computational complexity theory
At the same time, isomorphism for many special classes of graphs can be solved in polynomial time, and in practice graph isomorphism can often be solved
Graph_isomorphism_problem
Heuristic test for graph isomorphism
In graph theory, the Weisfeiler Leman graph isomorphism test is a heuristic test for the existence of an isomorphism between two graphs G and H. It is
Weisfeiler Leman graph isomorphism test
Weisfeiler_Leman_graph_isomorphism_test
Task in computational graph theory
from a solution to the graph canonization problem, one could also solve the problem of graph isomorphism: to test whether two graphs G and H are isomorphic
Graph_canonization
Graph representing edges of another graph
isomorphisms of the graphs and isomorphisms of their line graphs. Analogues of the Whitney isomorphism theorem have been proven for the line graphs of multigraphs
Line_graph
Hungarian-American mathematician and computer scientist
in 2017. abstract We show that the Graph Isomorphism (GI) problem and the related problems of String Isomorphism (under group action) (SI) and Coset
László_Babai
Mapping a graph onto itself without changing edge-vertex connectivity
is, it is a graph isomorphism from G to itself. Automorphisms may be defined in this way both for directed graphs and for undirected graphs. The composition
Graph_automorphism
Problem in theoretical computer science
theoretical computer science, the subgraph isomorphism problem is a computational task in which two graphs G {\displaystyle G} and H {\displaystyle H}
Subgraph_isomorphism_problem
constitutes a graph isomorphism. Fractional isomorphism is the coarsest of several different relaxations of graph isomorphism. Whereas the graph isomorphism problem
Fractional_graph_isomorphism
In mathematics, invertible homomorphism
with a unique isomorphism. The isomorphism theorems provide canonical isomorphisms that are not unique. The term isomorphism is mainly used for algebraic
Isomorphism
Unsolved problem in computer science
"Graph isomorphism is in SPP". Information and Computation. 204 (5): 835–852. doi:10.1016/j.ic.2006.02.002. Schöning, Uwe (1988). "Graph isomorphism is
P_versus_NP_problem
Property of graphs that depends only on abstract structure
polynomial of a graph. Easily computable graph invariants are instrumental for fast recognition of graph isomorphism, or rather non-isomorphism, since for
Graph_property
Topics referred to by the same term
Look up isomorphism or isomorph in Wiktionary, the free dictionary. Isomorphism or isomorph may refer to: Isomorphism, in mathematics, logic, philosophy
Isomorphism_(disambiguation)
testing whether two graphs are isomorphic. While it solves graph isomorphism on almost all graphs, there are graphs such as all regular graphs that cannot be
Colour_refinement_algorithm
Class of artificial neural networks
expressive as the Weisfeiler Leman graph isomorphism test. In practice, this means that there exist different graph structures that cannot be distinguished
Graph_neural_network
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)
Tree graph with one central node and leaves of length 1
the exceptional cases of the Whitney graph isomorphism theorem: in general, graphs with isomorphic line graphs are themselves isomorphic, with the exception
Star_(graph_theory)
Graph that can be embedded in the plane
also graph isomorphism problem). Any planar graph on n nodes has at most 8(n-2) maximal cliques, which implies that the class of planar graphs is a class
Planar_graph
Estimate of time taken for running an algorithm
length of the input is n {\displaystyle n} . Another example was the graph isomorphism problem, which the best known algorithm from 1982 to 2016 solved in
Time_complexity
Decision problem
isomorphism problem is the decision problem of determining whether two given finite group presentations refer to isomorphic groups. The isomorphism problem
Group_isomorphism_problem
Inherent difficulty of computational problems
"Graph isomorphism is in SPP", Information and Computation, 204 (5): 835–852, doi:10.1016/j.ic.2006.02.002. Schöning, Uwe (1988), "Graph Isomorphism is
Computational complexity theory
Computational_complexity_theory
Graph which is isomorphic to its complement
of checking whether a given graph is self-complementary are polynomial-time equivalent to the general graph isomorphism problem. Sachs, Horst (1962)
Self-complementary_graph
Problem of finding similarity between graphs
and the model graph. The case of exact graph matching is known as the graph isomorphism problem. The problem of exact matching of a graph to a part of
Graph_matching
Complexity class
two problems: Graph Isomorphism: Is graph G1 isomorphic to graph G2? Subgraph Isomorphism: Is graph G1 isomorphic to a subgraph of graph G2? The Subgraph
NP-completeness
Graph defined from a mathematical group
In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group, is a graph that encodes the abstract
Cayley_graph
NP-complete graph problem
complexity theory and graph theory, induced subgraph isomorphism is an NP-complete decision problem that involves finding a given graph as an induced subgraph
Induced subgraph isomorphism problem
Induced_subgraph_isomorphism_problem
them; see isomorphism. isomorphism A graph isomorphism is a one-to-one incidence preserving correspondence of the vertices and edges of one graph to the
Glossary_of_graph_theory
Infinite graph containing all countable graphs
In the mathematical field of graph theory, the Rado graph, Erdős–Rényi graph, or random graph is a countably infinite graph that can be constructed (with
Rado_graph
Python module
shortest path, etc. Support for several graph-theoretical algorithms: such as graph isomorphism, subgraph isomorphism, minimum spanning tree, connected components
Graph-tool
List of unsolved computational problems
quantum computer? Can the graph isomorphism problem be solved in polynomial time on a classical computer? The graph isomorphism problem involves determining
List of unsolved problems in computer science
List_of_unsolved_problems_in_computer_science
Complexity class of problems
are considered good candidates for being NP-intermediate are the graph isomorphism problem, and decision versions of factoring and the discrete logarithm
NP-intermediate
Graph structure studied in group theory
The cycle graph of a group is not uniquely determined up to graph isomorphism; nor does it uniquely determine the group up to group isomorphism. That is
Cycle_graph_(algebra)
Proving validity without revealing other data
questions to ask Peggy. He can either ask her to show the isomorphism between H and G (see graph isomorphism problem), or he can ask her to show a Hamiltonian
Zero-knowledge_proof
Fundamental unit of which graphs are formed
map any vertex to any other vertex. In the context of graph enumeration and graph isomorphism it is important to distinguish between labeled vertices
Vertex_(graph_theory)
Area of discrete mathematics
(NP-complete). One special case of subgraph isomorphism is the graph isomorphism problem. It asks whether two graphs are isomorphic. It is not known whether
Graph_theory
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
Very general problem in computer science
generalization of problems including factoring, discrete logarithm, graph isomorphism, and the shortest vector problem. This makes it especially important
Hidden_subgroup_problem
Creating a new graph from an existing graph
applied to the host graph by searching for an occurrence of the pattern graph (pattern matching, thus solving the subgraph isomorphism problem) and by replacing
Graph_rewriting
Undirected, connected, and acyclic graph
closed formula for the number t(n) of trees with n vertices up to graph isomorphism is known. The first few values of t(n) are 1, 1, 1, 1, 2, 3, 6, 11
Tree_(graph_theory)
Topics referred to by the same term
Isomorphism problem may refer to: graph isomorphism problem group isomorphism problem isomorphism problem of Coxeter groups This disambiguation page lists
Isomorphism_problem
Graph related to another graph by a covering map
graph-theoretic terms to a requirement that it be acyclic and connected; that is, a tree. The universal covering graph is unique (up to isomorphism)
Covering_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
Technique in parallel algorithms
tree isomorphism, graph isomorphism, maximal subtree isomorphism, common subexpression elimination, computing the 3-connected components of a graph, and
Tree_contraction
Graph in graph theory
problem of recognizing whether a graph is a lexicographic product is equivalent in complexity to the graph isomorphism problem. The lexicographic product
Lexicographic product of graphs
Lexicographic_product_of_graphs
popular classification criteria is graph isomorphism, not to be confused with crystallographic isomorphism. Two periodic graphs are often called topologically
Periodic_graph_(geometry)
American mathematician and computer scientist
at the University of Oregon. He is known for his research on the graph isomorphism problem and on algorithms for computational group theory. Luks did
Eugene_M._Luks
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)
Representation of a computer program
"HiddenCPG: Large-Scale Vulnerable Clone Detection Using Subgraph Isomorphism of Code Property Graphs". Proceedings of the ACM Web Conference 2022. pp. 755–766
Code_property_graph
of isomorphism. We ask: When are two graphs the same? (i.e., graph isomorphism) The graphs in question may be expressed differently in terms of graph equations
Graph_equation
In mathematics, a k-ultrahomogeneous graph is a graph in which every isomorphism between two of its induced subgraphs of at most k vertices can be extended
Homogeneous_graph
Method for solving one problem using another
consists of the problems that can be reduced to the graph isomorphism problem. Since graph isomorphism is known to belong both to NP and co-AM, the same
Polynomial-time_reduction
for each size) and the set of unrooted binary plane trees (up to graph isomorphism, with a fixed ordering of the leaves, and with size given by the number
Combinatorial_class
Peruvian mathematician (born 1977)
error in the proof of the quasipolynomial time algorithm for the graph isomorphism problem that was announced by László Babai in 2015. Babai subsequently
Harald_Helfgott
Open-source data analytics cluster computing framework
Malak, Michael (14 June 2016). "Finding Graph Isomorphisms In GraphX And GraphFrames: Graph Processing vs. Graph Database". slideshare.net. sparksummit
Apache_Spark
Undirected graph acted on by a vertex-transitive cyclic group of symmetries
neighbors are x ± 2, x ± 3, and x ± 5 modulo 16. These two graphs are isomorphic, but their isomorphism cannot be realized by a linear map. Toida's conjecture
Circulant_graph
of accepting paths, we can easily solve graph isomorphism. In fact, it was later shown that graph isomorphism is low for ZPPNP. Amplified PP is low for
Low_(complexity)
Convex hull of a finite set of points in a Euclidean space
the graph isomorphism problem. However, it is also possible to translate these problems in the opposite direction, showing that polytope isomorphism testing
Convex_polytope
Generalization of graph theory
(i)}} The bijection ϕ {\displaystyle \phi } is then called the isomorphism of the graphs. Note that H ≃ G {\displaystyle H\simeq G} if and only if H ∗
Hypergraph
Property of artificial neural networks
used. Universal function approximation on graphs (or rather on graph isomorphism classes) by popular graph convolutional neural networks (GCNs or GNNs)
Universal approximation theorem
Universal_approximation_theorem
Binary operation in graph theory
In graph theory, the modular product of graphs G and H is a graph formed by combining G and H that has applications to subgraph isomorphism. It is one
Modular_product_of_graphs
Assignment of colors to graph vertices that destroys all symmetries
least as hard as graph automorphism, but no harder than graph isomorphism". A coloring of a given graph is distinguishing for that graph if and only if
Distinguishing_coloring
Type of permutation of a set of elements
December 2011. Lubiw, Anna (1981). "Some NP-complete problems similar to graph isomorphism". SIAM Journal on Computing. 10 (1): 11–21. doi:10.1137/0210002. MR 0605600
Derangement
Topics referred to by the same term
on blood glucose Gender incongruence GI, a complexity class in the graph isomorphism problem .gi, the ccTLD for Gibraltar Gi (prefix symbol) (gibi), a
GI
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)
Canadian mathematician and computer scientist
algorithms for graph isomorphism. Algorithmic and structural properties of complement reducible graphs. Properties of asteroidal triple-free graphs. An algorithm
Derek_Corneil
Part of the mathematical subject of group theory
{\mathbf {A} }}} . More precisely, there is a group isomorphism σ: G → π1(A, v) and a graph isomorphism j : X → A ~ {\displaystyle j:X\to {\tilde {\mathbf
Bass–Serre_theory
Logical formulation of graph properties
subgraph isomorphism problem for a fixed subgraph H {\displaystyle H} asks whether H {\displaystyle H} appears as a subgraph of a larger graph G {\displaystyle
Logic_of_graphs
Directed graph with reversed edges
mathematical and algorithmic study of graph theory, the converse, transpose or reverse of a directed graph G is another directed graph on the same set of vertices
Transpose_graph
Type of electronic circuit design software
early as 1975. These early programs operated mainly on the level of graph isomorphism, checking whether the schematic and layout were indeed identical.
Layout_versus_schematic
Computational complexity class
announced but not fully published include: The graph isomorphism problem, determining whether two graphs can be made equal to each other by relabeling
Quasi-polynomial_time
induced subgraph isomorphism problem, which arises when k equals the number of vertices in the smaller of G and H, so that this entire graph must appear as
Maximum common induced subgraph
Maximum_common_induced_subgraph
Type of sub-graph
mapping f is called an isomorphism between G and G′. When G″ ⊂ G and there exists an isomorphism between the sub-graph G″ and a graph G′, this mapping represents
Network_motif
Branch of computational complexity theory
parameterizations which are fixed parameter tractable. Similarly, problems like Graph Isomorphism which are likely not NP-hard admit tractable parameterizations by
Parameterized_complexity
Directed graph isomorphic to its own transpose graph
to itself by the isomorphism or to group more than two vertices in a cycle of isomorphism. A path or cycle in a skew-symmetric graph is said to be regular
Skew-symmetric_graph
Square matrix used to represent a graph or network
determinant and trace. These can therefore serve as isomorphism invariants of graphs. However, two graphs may possess the same set of eigenvalues but not
Adjacency_matrix
crystallography, a periodic graph or crystal net is a three-dimensional periodic graph, i.e., a three-dimensional Euclidean graph whose vertices or nodes
Periodic graph (crystallography)
Periodic_graph_(crystallography)
804655. Norris, Nancy (1995). "Universal covers of graphs: Isomorphism to depth n−1 implies isomorphism to all depths". Discrete Applied Mathematics. 56:
Fibrations_of_graphs
British mathematician (1924–2019)
primarily on enumeration of graphs, graph isomorphism, chromatic polynomials, and particularly, the use of computers in graph-theoretical research. Read's
Ronald_C._Read
Structure-preserving correspondence between node-link graphs
bijection, and its inverse function f −1 is also a graph homomorphism, then f is a graph isomorphism. Covering maps are a special kind of homomorphisms
Graph_homomorphism
Venezuelan computer scientist
Vijay Vazirani, Luis von Ahn, and Ryan Williams. List of Venezuelans Graph isomorphism problem Non-interactive zero-knowledge proof Quantum coin flipping
Manuel_Blum
Statistical models for network analysis
four graph isomorphism classes: the graph with zero edges, three graphs with exactly one edge, three graphs with exactly two edges, and the graph with
Exponential family random graph models
Exponential_family_random_graph_models
Mapping which preserves all topological properties of a given space
Diffeomorphism – Isomorphism of differentiable manifolds Uniform isomorphism – Uniformly continuous homeomorphism is an isomorphism between uniform spaces
Homeomorphism
combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, mathematical logic, number theory, set theory, Ramsey
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Type of randomized algorithm
algorithms were introduced by László Babai in 1979, in the context of the graph isomorphism problem, as a dual to Monte Carlo algorithms. Babai introduced the
Las_Vegas_algorithm
Maximum number of colors in a greedy graph coloring
chordal graphs and claw-free graphs, and also (using general results on subgraph isomorphism in sparse graphs to search for atoms) for graphs of bounded
Grundy_number
Standard representation of a mathematical object
from a solution to the graph canonization problem, one could also solve the problem of graph isomorphism: to test whether two graphs G and H are isomorphic
Canonical_form
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
Algebraic Graph Theory, Graduate Texts in Math., Vol. 207, Springer-Verlag, New York. Brendan McKay (1981), Practical graph isomorphism, Congressus
Equitable_partition
Topics referred to by the same term
glucose-dependent insulinotropic polypeptide Genome India Project Graph isomorphism problem GSM Interworking Profile, a telecommunications standard Francisco
GIP
Complexity class
1007/978-3-319-32162-2_1. ISBN 9783319321622. See Section 2.2.4 Factoring and Graph Isomorphism, pp. 19–20 of book (pp. 17–18 of linked version). Complexity Zoo:
Co-NP
Theorem classifying finite simple groups
groups. A breakthrough in the best known theoretical algorithm for the graph isomorphism problem in 1982 The Schreier conjecture The Signalizer functor theorem
Classification of finite simple groups
Classification_of_finite_simple_groups
Graph of numbers differing by a square
x ± 4 (mod 13). The Paley graphs are self-complementary: the complement of any Paley graph is isomorphic to it. One isomorphism is via the mapping that
Paley_graph
Visual representations of a store's products or services
Stefano, Luigi (2017). "Product Recognition in Store Shelves as a Sub-Graph Isomorphism Problem". Image Analysis and Processing – ICIAP 2017. Lecture Notes
Planogram
Soviet mathematician and computer scientist (1940–2012)
scientist who is known for the development of the Weisfeiler Leman graph isomorphism test together with Boris Weisfeiler published in 1968. He contributed
Andrey_Leman
Computer algebra system
speeds for most index contractions with an approach based on the graph isomorphism problem rather than canonicalisation. Free and open-source software
Cadabra_(computer_program)
Graph made from disjoint union of complete graphs
a cluster graph is formed from cliques that are all the same size, the overall graph is a homogeneous graph, meaning that every isomorphism between two
Cluster_graph
Natural number
294 groups of order 64 up to isomorphism. This was later disproven; there are 267 groups of order of 64 up to isomorphism. See List of incomplete proofs
294_(number)
16-regular graph with 27 vertices and 216 edges
eight-dimensional representation described above. A graph is defined to be k-ultrahomogeneous if every isomorphism between two of its induced subgraphs of at most
Schläfli_graph
One of two different regular graphs with 16 vertices
meaning that every isomorphism between two connected induced subgraphs can be extended to an automorphism of the whole graph. The Clebsch graph is Hamiltonian
Clebsch_graph
Graph made from a subset of another graph's nodes and their edges
The induced subgraph isomorphism problem is a form of the subgraph isomorphism problem in which the goal is to test whether one graph can be found as an
Induced_subgraph
travel, tourism, insurance
GRAPH ISOMORPHISM
GRAPH ISOMORPHISM
Girl/Female
Afghan, Arabic, Hebrew, Indian, Muslim, Parsi, Sanskrit
Grape Presser; World; Song; Universe
Boy/Male
Muslim
Grape
Girl/Female
Tamil
Kaslunira | கஸà¯à®²à¯à®‚நீரா
Grape, Belonging to kashmir
Kaslunira | கஸà¯à®²à¯à®‚நீரா
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
Hindu, Indian, Punjabi, Sikh
From Kashmir; Grape
Girl/Female
Hindu
Grape, Belonging to kashmir
Female
Thai/Siamese
Thai name A-GUN means "grape."
Boy/Male
Afghan, Hebrew, Indian, Parsi, Sanskrit
Grape Presser; World; Song
Girl/Female
Indian
Grape like
Girl/Female
Indian
Grape vine
Boy/Male
Biblical
A grape, a knot.
Boy/Male
African, Arabic
Grape Vines
Girl/Female
Muslim
Grape vine
Girl/Female
Muslim
Grape like
Boy/Male
Hebrew, Hindu, Indian, Marathi
Grape Cluster
Boy/Male
Indian
Grape
Biblical
a grape; a knot
Girl/Female
Arabic, Assamese, Hindu, Indian, Kannada, Malayalam, Marathi, Muslim, Telugu
Grape
Boy/Male
Arabic, Modern
Grape
Boy/Male
Biblical
A grape, a knot.
GRAPH ISOMORPHISM
GRAPH ISOMORPHISM
GRAPH ISOMORPHISM
GRAPH ISOMORPHISM
GRAPH ISOMORPHISM
GRAPH ISOMORPHISM
GRAPH ISOMORPHISM
travel, tourism, insurance