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Assignment of labels to elements of a graph
discipline of graph theory, a graph labeling is the assignment of labels, traditionally represented by integers, to edges and/or vertices of a graph. Formally
Graph_labeling
Type of graph vertex labeling
A graph which admits a graceful labeling is called a graceful graph. The name "graceful labeling" is due to Solomon W. Golomb; this type of labeling was
Graceful_labeling
Task in computational graph theory
a given graph G. A canonical form is a labeled graph Canon(G) that is isomorphic to G, such that every graph that is isomorphic to G has the same canonical
Graph_canonization
Algorithmic application of graph theory
application of graph theory, where subsets of connected components are uniquely labeled based on a given heuristic. Connected-component labeling is not to
Connected-component_labeling
Methodic assignment of colors to elements of a graph
the same color. Graph coloring is a special case of graph labeling. In its simplest form, it is a way of coloring the vertices of a graph such that no two
Graph_coloring
Graph of triangles with a shared vertex
the mathematical field of graph theory, the friendship graph (or Dutch windmill graph or n-fan) Fn is a planar, undirected graph with 2n + 1 vertices and
Friendship_graph
Directed graph with no directed cycles
In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it
Directed_acyclic_graph
or edges have labels. The terms vertex-labeled or edge-labeled may be used to specify which objects of a graph have labels. Graph labeling refers to several
Glossary_of_graph_theory
Mathematical model used by graph-oriented databases
A property graph, labeled property graph, or attributed graph is a data model of various graph-oriented databases, where pairs of entities are associated
Property_graph
One of two types of graph
and a single edge. The 7-page book graph of this type provides an example of a graph with no harmonious labeling. A second type, which might be called
Book_(graph_theory)
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 family made by joining complete graphs at a universal node
field of graph theory, the windmill graph Wd(k,n) is an undirected graph constructed for k ≥ 2 and n ≥ 2 by joining n copies of the complete graph Kk at
Windmill_graph
Maximal subgraph whose vertices can reach each other
not. The components of a graph can be constructed in linear time, and a special case of the problem, connected-component labeling, is a basic technique in
Component_(graph_theory)
Bijection between the vertex set of two graphs
In graph theory, an isomorphism of graphs G and H is a bijection between the vertex sets of G and H f : V ( G ) → V ( H ) {\displaystyle f\colon V(G)\to
Graph_isomorphism
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
Set of integers in graph theory
a type of graph labeling called a friendly labeling. A friendly labeling of an n-vertex undirected graph G = (V,E) is defined to be an assignment of
Friendly-index_set
Abstract data type in computer science
science, a graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from the field of graph theory within
Graph_(abstract_data_type)
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)
Franklin graph Frucht graph Goldner–Harary graph Golomb graph Grötzsch graph Harries graph Harries–Wong graph Herschel graph Hoffman graph Hofman Graph H(12
List_of_graphs
Linear algebra aspects of graph theory
on the vertex labeling, its spectrum is a graph invariant, although not a complete one. Spectral graph theory is also concerned with graph parameters that
Spectral_graph_theory
Database using graph structures for queries
A graph database (GDB) is a database that uses graph structures for semantic queries with nodes, edges, and properties to represent and store data. A key
Graph_database
theorem Girth Graph drawing Graph homomorphism Graph labeling Graceful labeling Graph partition Graph pebbling Graph property Graph reduction Graph-structured
List_of_graph_theory_topics
Graph with multiple edges between two vertices
vertices and the same arc label (note that this notion of a labeled graph is different from the notion given by the article graph labeling). Multidimensional
Multigraph
Type of graph labeling
In graph theory, an edge-graceful labeling is a type of graph labeling for simple, connected graphs in which no two distinct edges connect the same two
Edge-graceful_labeling
Fundamental unit of which graphs are formed
specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set
Vertex_(graph_theory)
Graph formed by complementation and disjoint union
In graph theory, a cograph, or complement-reducible graph, or P4-free graph, is a graph that can be generated from the single-vertex graph K1 by complementation
Cograph
Unsolved problem in computational complexity theory
computer science Can the graph isomorphism problem be solved in polynomial time? More unsolved problems in computer science The graph isomorphism problem is
Graph_isomorphism_problem
Algorithmically defined graph
Intersection graphs An interval graph is the intersection graph of a set of line segments in the real line. It may be given an adjacency labeling scheme in
Implicit_graph
Special case of graph labeling in graph theory
In graph theory, a weak coloring is a special case of a graph labeling. A weak k-coloring of a graph G = (V, E) assigns a color c(v) ∈ {1, 2, ..., k}
Weak_coloring
Mapping a graph onto itself without changing edge-vertex connectivity
sparse graphs, e.g., SAUCY processes some graphs with millions of vertices in mere seconds. However, BLISS and NAUTY can also produce Canonical Labeling, whereas
Graph_automorphism
American mathematician and mathematics educator
mathematician and mathematics educator. Her research concerns graph theory and graph labeling, and she is also an advocate of inquiry-based learning in mathematics
Alison_Marr
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
Node labeling problem in graph theory
placement is called linear graph arrangement, linear graph layout or linear graph placement. It may be formalized as labeling the n {\displaystyle n} vertices
Graph_bandwidth
Cartesian product of complete graphs
test whether a graph is a Hamming graph, and in the case that it is, find a labeling of it with tuples that realizes it as a Hamming graph. Brouwer, Andries
Hamming_graph
Representation of molecules in terms of graph theory
structural formula of a chemical compound in terms of graph theory. A chemical graph is a labeled graph whose vertices correspond to the atoms of the compound
Molecular_graph
Solid with twenty equal triangular faces
PMC 8156859. PMID 34063479. Gallian, Joseph A. (1998). "A dynamic survey of graph labeling". Electronic Journal of Combinatorics. 5: Dynamic Survey 6, 43 pp. (389
Regular_icosahedron
Property of graphs that depends only on abstract structure
representations such as particular labellings or drawings of the graph. While graph drawing and graph representation are valid topics in graph theory, in order to focus
Graph_property
File format
DOT is a graph description language, developed as a part of the Graphviz project. DOT graphs are typically stored as files with the .gv or .dot filename
DOT (graph description language)
DOT_(graph_description_language)
graphs must be at least n − 1 {\displaystyle n-1} . Graham and Pollak study a more general graph labeling problem, in which the vertices of a graph should
Graham–Pollak_theorem
Class of artificial neural networks
Graph neural networks (GNNs) are artificial neural networks designed for tasks whose inputs are graphs. Because graphs usually do not have a canonical
Graph_neural_network
difference being the starting index for labels (0 versus 1). This means that if a graph has L(2,1)-labeling number k, it has radio coloring number k
Radio_coloring
and conversely if a labeling scheme exists then a universal graph may be constructed having a vertex for every possible label. In older mathematical
Universal_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
Complexity class of problems
bisection Deciding whether a graph admits a graceful labeling Recognizing leaf powers and k-leaf powers Recognizing graphs of bounded clique-width Testing
NP-intermediate
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)
A magic graph is a graph whose edges are labelled by the first q positive integers, where q is the number of edges, so that the sum over the edges incident
Magic_graph
Computer science algorithm
for many graph-related algorithms, including topological sorts and planarity testing. Input: A graph G and a vertex v of G. Output: A labeling of the edges
Graph_traversal
Graph that misrepresents data
In statistics, a misleading graph, also known as a distorted graph, is a graph that misrepresents data, constituting a misuse of statistics and with the
Misleading_graph
as many rows as nodes present within the graph. For each row (each node), a label will be calculated. A label is a string containing the distance information
Hub_labels
Vertex coloring where no two linked nodes have the same color pairing
In graph theory, a harmonious coloring is a (proper) vertex coloring in which every pair of colors appears on at most one pair of adjacent vertices. It
Harmonious_coloring
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
Binary operation in graph theory
planar graphs have bounded queue number, small universal graphs and concise adjacency labeling schemes, and bounded nonrepetitive chromatic number and
Strong_product_of_graphs
Polytope whose vertices represent permutations
See, e.g., Ziegler (1995), p. 18. Ziegler (1995), p. 200. This Cayley graph labeling is shown, e.g., by Ziegler (1995). Baek, Adams & Dolson (2013). Baek
Permutohedron
Special labeling in graph theory
special graph labeling where each incidence of an edge with a vertex is assigned a color under certain constraints. Below G denotes a simple graph with non-empty
Incidence_coloring
Graphical representation of a computer program or algorithm
In computer science, a control-flow graph (CFG) is a representation, using graph notation, of all paths that might be traversed through a function during
Control-flow_graph
In graph theory, a sum coloring of a graph is a labeling of its vertices by positive integers, with no two adjacent vertices having equal labels, that
Sum_coloring
Creating a new graph from an existing graph
computer science, graph transformation, or graph rewriting, concerns the technique of creating a new graph out of an original graph algorithmically. It
Graph_rewriting
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
Problem in natural language processing and information retrieval
typically produce any such labels. Cluster labeling algorithms examine the contents of the documents per cluster to find a labeling that summarize the topic
Cluster_labeling
Undirected graph acted on by a vertex-transitive cyclic group of symmetries
Vilfred. Define a circulant numbering of a circulant graph to be a labeling of the vertices of the graph by the numbers from 0 to n − 1 in such a way that
Circulant_graph
Isometric subgraph of a hypercube
graph is equal to the Hamming distance between their labels. Such a labeling is called a Hamming labeling; it represents an isometric embedding of the partial
Partial_cube
Python library for graphs and networks
NetworkX is a Python library for studying graphs and networks. NetworkX is free software released under the BSD-new license. NetworkX began development
NetworkX
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
Type of dominating set in graph theory
Dominating set Graph labeling Cockayne, E. J.; Dreyer, P. A.; Hedetniemi, S. M.; Hedetniemi, S. T. (2004), "Roman domination in graphs", Discrete Mathematics
Roman_dominating_set
Algorithm to search the nodes of a graph
tree or graph data structures. The algorithm starts at the root node (selecting some arbitrary node as the root node in the case of a graph) and explores
Depth-first_search
Algorithm for finding shortest paths
an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent, for example, a road network. It was conceived by computer
Dijkstra's_algorithm
Complete bipartite cut in a graph
In graph theory, a split of an undirected graph is a cut whose cut-set forms a complete bipartite graph. A graph is prime if it has no splits. The splits
Split_(graph_theory)
Graph representing intersections between given sets
In graph theory, an intersection graph is a graph that represents the pattern of intersections of a family of sets. Any graph can be represented as an
Intersection_graph
Two closely related models for generating random graphs
the mathematical field of graph theory, the Erdős–Rényi models are two closely related models for generating random graphs and the evolution of a random
Erdős–Rényi_model
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)
Approximate nearest neighbor search algorithm
datasets. HNSW stores vectors in a graph. Each vector is a node, and links connect it to some nearby vectors. The graph has several layers: upper layers
Hierarchical navigable small world
Hierarchical_navigable_small_world
Directed graph representing dependencies
mathematics, computer science and digital electronics, a dependency graph is a directed graph representing dependencies of several objects towards each other
Dependency_graph
In graph theory, the Krackhardt kite graph is a simple graph with ten nodes. The graph is named after David Krackhardt, a researcher of social network
Krackhardt_kite_graph
Query language for property graphs
GQL (Graph Query Language) is a standardized query language for property graphs first described in ISO/IEC 39075, released in April 2024 by ISO/IEC. The
Graph_Query_Language
Operation in graph theory
In graph theory, the Cartesian product G □ H of graphs G and H is a graph such that: the vertex set of G □ H is the Cartesian product V(G) × V(H); and
Cartesian_product_of_graphs
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)
Algorithm to search the nodes of a graph
for the graph itself, which may vary depending on the graph representation used by an implementation of the algorithm. When working with graphs that are
Breadth-first_search
Optimization technique
for a proposed fix). Multiple labels: Graph cuts is only able to find a global optimum for binary labeling (i.e., two labels) problems, such as foreground/background
Graph cuts in computer vision and artificial intelligence
Graph_cuts_in_computer_vision_and_artificial_intelligence
Computational problem of graph theory
In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights
Shortest_path_problem
Topics referred to by the same term
program to detect and manage a serious error condition Graceful labeling, a type of graph labeling Graceful degradation, a property enabling a system to continue
Graceful_(disambiguation)
Formalism for knowledge representation
logic (predicate calculus) is represented by a labeled graph. A linear notation, called the Conceptual Graph Interchange Format (CGIF), has been standardized
Conceptual_graph
American mathematician
America. ISBN 978-0-88385-349-8. Gallian, Joseph A. "A Dynamic Survey of Graph Labeling". The Electronic Journal of Combinatorics. doi:10.37236/27. "Biography
Joseph_Gallian
Two-sided graph with consecutive neighbors
u_{i}} . A biconvex graph is called forward-convex if there exists a labeling such that V {\displaystyle V} is convex and the labeling has the forward property:
Convex_bipartite_graph
Graph generated by a random process
In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability
Random_graph
In the mathematical field of graph theory, a word-representable graph is a graph that can be characterized by a word (or sequence) whose entries alternate
Word-representable_graph
Graph database system
Sparksee (formerly known as DEX) is a high-performance and scalable graph database management system written in C++. From version 6.0, Sparksee has shifted
Sparksee_(graph_database)
Square matrix used to represent a graph or network
In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether
Adjacency_matrix
Graph with directed and undirected edges
path is a cycle. A mixed graph is acyclic if it does not contain a cycle. Mixed graph coloring can be thought of as labeling or an assignment of k different
Mixed_graph
Adjacent subset of an undirected graph
In graph theory, a clique (/ˈkliːk/ or /ˈklɪk/) is a subset of vertices of an undirected graph such that every two distinct vertices in the clique are
Clique_(graph_theory)
Matrix representation of a graph
In the mathematical field of graph theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix, or discrete Laplacian
Laplacian_matrix
Directed graph whose edges are labelled invertibly by elements of a group
In graph theory, a voltage graph is a directed graph whose edges are labelled invertibly by elements of a group. It is formally identical to a gain graph
Voltage_graph
On bipartite matching and vertex cover
In the mathematical area of graph theory, Kőnig's theorem, proved by Dénes Kőnig (1931), describes an equivalence between the maximum matching problem
Kőnig's theorem (graph theory)
Kőnig's_theorem_(graph_theory)
Longest distance between tree vertices
Diameter (graph theory) Distance (graph theory) Tree (graph theory) Median graph Chartrand, Gary; Erwin, David; Zhang, Ping (2005). "A graph labeling problem
Triameter_(graph_theory)
Pan-genome Graph Construction Methodology
Pan-genome graph construction is the process of creating a graph-based representation of the collective genome (the pan-genome) of a species or a group
Pan-genome_graph_construction
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
Assignment of colors to graph vertices that destroys all symmetries
In graph theory, a distinguishing coloring or distinguishing labeling of a graph is an assignment of colors or labels to the vertices of the graph that
Distinguishing_coloring
Graphical representation of data
A chart (sometimes known as a graph) is a graphical representation for data and information visualization, in which "the data is represented by symbols
Chart
Clustering and community detection algorithm
well-connected. Consider, for example, the following graph: Three communities are present in this graph (each color represents a community). Additionally
Leiden_algorithm
Measure of similarity between two graphs
of the graph are labeled and whether the edges are directed. Generally, given a set of graph edit operations (also known as elementary graph operations)
Graph_edit_distance
Abstract mathematical system of two types of objects and a relation between them
to a bipartite graph called the Levi graph or incidence graph of the structure. As any bipartite graph is two-colorable, the Levi graph can be given a
Incidence_structure
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GRAPH LABELING
GRAPH LABELING
GRAPH LABELING
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GRAPH LABELING
GRAPH LABELING
GRAPH LABELING
GRAPH LABELING
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