mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context...

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...

In graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected acyclic undirected...

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 need...

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...

In graph theory, a component of an undirected graph is a connected subgraph that is not part of any larger connected subgraph. The components of any graph...

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...

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...

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...

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...

In the mathematical area of graph theory, a clique (/ˈkliːk/ or /ˈklɪk/) is a subset of vertices of an undirected graph such that every two distinct vertices...

In graph theory, a path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices which, by most definitions, are all distinct...

In mathematics, spectral graph theory is the study of the properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors...

In graph theory, a cycle in a graph is a non-empty trail in which only the first and last vertices are equal. A directed cycle in a directed graph is...

essence, extremal graph theory studies how global properties of a graph influence local substructure. Results in extremal graph theory deal with quantitative...

bipartite graph Disperser Expander Extractor Bivariegated graph Cage (graph theory) Cayley graph Circle graph Clique graph Cograph Common graph Complement...

Algebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs. This is in contrast to geometric, combinatoric...

In graph theory, a loop (also called a self-loop or a buckle) is an edge that connects a vertex to itself. A simple graph contains no loops. Depending...

In graph theory, a cut is a partition of the vertices of a graph into two disjoint subsets. Any cut determines a cut-set, the set of edges that have one...

mathematical field of graph theory, the distance between two vertices in a graph is the number of edges in a shortest path (also called a graph geodesic) connecting...

Geometric graph theory in the broader sense is a large and amorphous subfield of graph theory, concerned with graphs defined by geometric means. In a stricter...

In graph theory, a star Sk is the complete bipartite graph K1,k : a tree with one internal node and k leaves (but no internal nodes and k + 1 leaves when...

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...

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...

topological graph theory is a branch of graph theory. It studies the embedding of graphs in surfaces, spatial embeddings of graphs, and graphs as topological...

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...

In graph theory, an arborescence is a directed graph where there exists a vertex r (called the root) such that, for any other vertex v, there is exactly...

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...

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...

discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential...