topology, closed graph is a property of functions. A function f : X → Y between topological spaces has a closed graph if its graph is a closed subset of...

In graph theory, a graph property or graph invariant is a property of graphs that depends only on the abstract structure, not on graph representations...

A property graph, labeled property graph, or attributed graph is a data model of various graph-oriented databases, where pairs of entities are associated...

analysis, the closed graph theorem is a result connecting the continuity of a linear operator to a topological property of their graph. Precisely, the...

mathematics, a closed linear operator or often a closed operator is a linear operator whose graph is closed (see closed graph property). It is a basic...

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...

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...

trail in which the first and last vertices are equal (closed trail). Let G = (V, E, Φ) be a graph. A circuit is a non-empty trail (e1, e2, ..., en) with...

every graph property preserved by deletions and contractions may be recognized in polynomial time. Other results and conjectures involving graph minors...

context. These properties are particularly considered in topology and graph theory, but also in set theory. In topology, a topological property is said to...

some number of vertices (at least 3, if the graph is simple) connected in a closed chain. The cycle graph with n vertices is called Cn. The number of...

of points on the graph converges, its limit point must also belong to the graph. This concept, related to the closed graph property in functional analysis...

Borel graph theorem is generalization of the closed graph theorem that was proven by L. Schwartz. The Borel graph theorem shows that the closed graph theorem...

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...

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...

relationship, form a well-quasi-ordering. Equivalently, every family of graphs that is closed under taking minors can be defined by a finite set of forbidden...

directed graph, each edge has an orientation, from one vertex to another vertex. A path in a directed graph is a sequence of edges having the property that...

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...

nontrivial symmetries. Formally, an automorphism of a graph is a permutation p of its vertices with the property that any two vertices u and v are adjacent if...

graph theory, an adjacent vertex of a vertex v in a graph is a vertex that is connected to v by an edge. The neighbourhood of a vertex v in a graph G...

embedding of the graph G, so it is a property of plane graphs (graphs that are already embedded in the plane) rather than planar graphs (graphs that may be...

states that these are the only graphs with planar covers. The existence of a planar cover is a minor-closed graph property, and so can be characterized...

In graph theory, a branch of mathematics, many important families of graphs can be described by a finite set of individual graphs that do not belong to...

Hadwiger's conjecture, YΔY-reducible graphs, and relations between treewidth and graph diameter. Apex graphs are closed under the operation of taking minors:...

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...

distinguish multiple concepts generalizing continuity, such as the closed graph property and upper and lower hemicontinuity. There are also various generalizations...

single edge. The family of graphs in which each component is a cactus is downwardly closed under graph minor operations. This graph family may be characterized...

In the study of graph algorithms, an implicit graph representation (or more simply implicit graph) is a graph whose vertices or edges are not represented...

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...

there are an odd number of such graphs on any even number of vertices. This, in turn, can be used to show that the property of having a universal vertex...