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A graph is a structure consisting of vertices and edges, where edges can be directed or undirected. Learn the definitions, properties, examples and applications of graphs and related concepts in graph theory.
Learn about graphs, mathematical structures that model pairwise relations between objects. Find out the differences between undirected and directed graphs, and see how to define and represent them with vertices, edges, loops and incidence functions.
A vertex is the fundamental unit of a graph, and its degree is the number of edges incident to it. Learn about different types of vertices, such as isolated, leaf, source, sink, simplicial, universal, cut, and more.
Learn about the concept of neighbourhood in graph theory, which refers to the vertices adjacent to a given vertex or a set of vertices. Find out how neighbourhoods are used in graph algorithms, clustering, local properties, and graph classes.
Graph labeling is the assignment of labels to vertices and/or edges of a graph. The concept of graph labeling was introduced by Alexander Rosa in 1967, and he also defined three types of labelings: α-, β-, and ρ-labelings.
A directed graph is a graph with directed edges, often called arcs, that connect vertices in a specific order. Learn about the different types of directed graphs, such as simple, loop-digraphs, oriented, acyclic, and weighted, and see examples and applications.
Contracting the edge between the indicated vertices, resulting in graph G / {uv}. In graph theory, an edge contraction is an operation that removes an edge from a graph while simultaneously merging the two vertices that it previously joined. Edge contraction is a fundamental operation in the theory of graph minors.
A bipartite graph is a graph whose vertices can be divided into two disjoint and independent sets, such that every edge connects a vertex in one set with a vertex in the other. Learn about the examples, properties, characterization, and applications of bipartite graphs in graph theory and other fields.