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Graph theory

Adjacency matrix

Square matrix used to represent a graph or network

Bellman–Ford algorithm

Algorithm for finding the shortest paths in graphs

Formula used in graph theory

Bipartite graph

Graph in which every vertex is connected to at least one other

Blossom algorithm

Algorithm for constructing maximum matchings on a graph

Bridge (graph theory)

Edge in node-link graph whose removal would disconnect the graph

Cage (graph theory)

Regular graph that has as few vertices as possible for its girth

Graph whose vertices and edges represent the elements of a group and their products with the generators of the group

Chromatic polynomial

Polynomial defined from a node-link graph, that counts the number of graph colorings as a function of the number of colors

Circulation problem

Generalization of network flow problems

Clique (graph theory)

Subset of the vertices of a node-link graph that are all adjacent to each other

Computational problem of finding cliques in a graph

Graph in which every two vertices are adjacent

Component (graph theory)

Maximal subgraph of a given node-link graph within which every two vertices may be connected by a path

Connectivity (graph theory)

Basic concept of graph theory

Graph with 28 vertices and 42 edges

Crossing number (graph theory)

The smallest number of edge crossings possible in a drawing of a node-link graph

Crossing number inequality

Theorem providing a lower bound to the crossing number; for sufficiently large graphs, the crossing number is not less than a constant times the cube of the number of edges divided by the square of the number of vertices

Cycle (graph theory)

Trail in which the only repeated vertices are the first and last

Degree (graph theory)

Number of edges incident to a given vertex in a node-link graph

Type of matrix in algebraic graph theory

Dijkstra's algorithm

Algorithm for finding shortest paths

Graph with oriented edges

Undirected graph

Edge contraction

Operation that removes an edge from a graph and combines its endpoints into a single vertex

A set of edges that touches every vertex of a graph

Trail in a finite graph which visits every edge exactly once

Algorithm for counting perfect matchings in planar graphs

Directed graph where each edge has a capacity and each edge receives a flow

Floyd–Warshall algorithm

Algorithm for finding all-pairs shortest paths in graphs, allowing some edge weights to be negative

Ford–Fulkerson algorithm

Algorithm to compute the maximum flow in a flow network (equivalently; the minimum cut)

Four color theorem

Statement in mathematics

Directed graph where edge-directions are labeled using group elements

Generalized Petersen graph

Family of cubic graphs formed from regular and star polygons

Girth (graph theory)

Length of a shortest cycle contained in the graph

Graph (discrete mathematics)

Mathematical structure consisting of vertices and edges connecting some pairs of vertices

Graph automorphism

Symmetry of a graph onto itself preserving the edge–vertex connectivity

Methodic assignment of colors to elements of a graph

Graph homomorphism

A structure-preserving correspondence between node-link graphs

Graph isomorphism

Bijection between the vertex set of two graphs

Graph isomorphism problem

Unsolved problem in computational complexity theory

Graph formed from another graph by deleting edges and vertices and contracting edges

Area of discrete mathematics

Hamiltonian path

Path in a graph that visits each vertex exactly once

Hamiltonian path problem

Problem of finding a cycle through all vertices of a graph

Handshaking lemma

Lemma that every node-link graph has an even number of odd-degree vertices

Held–Karp algorithm

Solution of the traveling salesman problem

Bipartite undirected graph

Homeomorphism (graph theory)

Concept in graph theory

Hopcroft–Karp algorithm

Algorithm for maximum cardinality matching in bipartite graphs

Number of matchings in a graph

Generalization of graph theory

Intersection graph

Non-oriented graph in which two nodes are linked if and only if the two parts of a common space and represented by these nodes have a non-empty intersection in that space

Kőnig's theorem (graph theory)

Theorem showing that maximum matching and minimum vertex cover are equivalent for bipartite graphs

Kruskal's algorithm

Minimum spanning forest algorithm that greedily adds edges

Kuratowski's theorem

Theorem characterizing planar graphs

Laplacian matrix

Matrix representation of a graph

Concept in graph theory

Lovász conjecture

Unproven conjecture, that every finite connected vertex-transitive graph contains a Hamiltonian path

Matching (graph theory)

Set of edges without common vertices

Matching polynomial

Graph polynomial generating numbers of matchings

Max-flow min-cut theorem

Concept in optimization theory

Maximum cardinality matching

A graph theory problem

Maximum flow problem

Computational problem in graph theory

Minimum-cost flow problem

Mathematical optimization problem

Multi-commodity flow problem

Flow network problem with multiple commodities between different source and sink nodes

Undirected graph which is permitted to have multiple edges but no loops

Nowhere-zero flow

Concept in graph theory

Path (graph theory)

Sequence of edges connecting a sequence of vertices in a graph, with no repeating vertices

Perfect matching

Graph theory term

Cubic graph with 10 vertices and 15 edges

Graph that can be embedded in the plane

Technique for drawing non-planar graphs

Prim's algorithm

Push–relabel maximum flow algorithm

Rainbow matching

Edge-colored graph matching where all edges have distinct colors

Where each vertex has the same number of neighbors

Seven Bridges of Königsberg

Classic problem in graph theory

Shortest path problem

Computational problem of graph theory

Snark (graph theory)

Bridgeless cubic graph with chromatic index equal to 4

Spectral graph theory

Linear algebra aspects of graph theory

Tait's conjecture

Disproven graph theory

Three utilities problem

Mathematical puzzle of avoiding crossings

Travelling salesman problem

NP-hard problem in combinatorial optimization

Tree (graph theory)

Undirected, connected and acyclic graph

Turán's brick factory problem

Problem of minimizing crossings in complete bipartite graphs

Tutte–Berge formula

A characterization of the size of a maximum matching in a graph

Subset of a graph's vertices, including at least one endpoint of every edge

Vizing's theorem

A theorem in graph coloring