Graph theory objects

unit connected by edges with other units in a graph, in graph theory

path in a graph that visits each vertex exactly once

trail in a graph which visits every edge exactly once

set of vertices in a graph, no two of which are adjacent

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

in graph theory, non-empty trail in which only the first and last vertices are equal

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

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

edge connecting a vertex to itself

a set of vertices in a node-link graph such that every vertex is either in the set or adjacent to it

another graph, formed from a subset of the vertices of the graph and all of the edges connecting pairs of vertices in that subset

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

set of vertices adjacent to a given vertex in a graph

mapping of a graph into a tree

a cut of a graph whose size is at least the size of any other cut

in graph theory, edges incident/directed between the same vertices

vertex of an undirected graph that is adjacent to all other vertices of the graph. It may also be called a dominating vertex, as it forms a one-element dominating set in the graph

problem of finding a minimal clique cover of a given graph

partition of the edges of a graph into disjoint spanning k-regular subgraphs

a cut of a graph that is minimal

set of all vertices of minimum eccentricity

assignment of integer labels to the vertices of a graph that uniquely identifies edges by the difference of their endpoint labels

independent set of graph vertices that is not a subset of any other independent set

graph path which is an induced subgraph

thumb|upright=1.2|A 1-forest (a maximal pseudoforest), formed by three 1-trees In graph theory, a pseudoforest is an undirected graph in which every connected component has at most one cycle. That is, it is a system of vertices and edges connecting pairs of vertices, such that no two cycles of consecutive edges share any vertex with each other, nor can any two cycles be connected to each other by a path of consecutive edges. A pseudotree is a connected pseudoforest.

a subset of the edges in a directed graph that includes at least one edge from each cycle

partition of graph into sequence of paths

assignment of a direction to each edge of a graph