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...

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 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...

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...

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...

of graph theory, a cubic graph is a graph in which all vertices have degree three. In other words, a cubic graph is a 3-regular graph. Cubic graphs are...

The theory of random graphs lies at the intersection between graph theory and probability theory. From a mathematical perspective, random graphs are used...

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

field of algebraic graph theory, the degree matrix of an undirected graph is a diagonal matrix which contains information about the degree of each vertex—that...

In the mathematical field of graph theory, a path graph (or linear graph) is a graph whose vertices can be listed in the order v1, v2, ..., vn such that...

In the mathematical field of graph theory, a graph G is symmetric or arc-transitive if, given any two ordered pairs of adjacent vertices ( u 1 , v 1 )...

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...

In graph theory, an Eulerian trail (or Eulerian path) is a trail in a finite graph that visits every edge exactly once (allowing for revisiting vertices)...

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 k-degenerate graph is an undirected graph in which every subgraph has at least one vertex of degree at most k {\displaystyle k} . That...

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

In graph theory, the diameter of a connected undirected graph is the farthest distance between any two of its vertices. That is, it is the diameter of...

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...

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...

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...

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...

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...

In graph theory, the girth of an undirected graph is the length of a shortest cycle contained in the graph. If the graph does not contain any cycles (that...

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, two graphs G {\displaystyle G} and G ′ {\displaystyle G'} are homeomorphic if there is a graph isomorphism from some subdivision of G...

geometric group theory. The structure and symmetry of Cayley graphs make them particularly good candidates for constructing expander graphs. Let G {\displaystyle...

of graph theory, a half-transitive graph is a graph that is both vertex-transitive and edge-transitive, but not symmetric. In other words, a graph is...