In graph theory, a connected graph G is said to be k-vertex-connected (or k-connected) if it has more than k vertices and remains connected whenever fewer...

smallest vertex cut. A graph is called k-vertex-connected or k-connected if its vertex connectivity is k or greater. More precisely, any graph G (complete...

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...

graph theory, a connected graph is k-edge-connected if it remains connected whenever fewer than k edges are removed. The edge-connectivity of a graph...

vertex is called the apex. A k-apex graph is a graph that can be made planar by the removal of k vertices. 2.  Synonym for universal vertex, a vertex...

the graph. A k-vertex-connected graph is often called simply a k-connected graph. A bipartite graph is a simple graph in which the vertex set can be partitioned...

In graph theory, a vertex subset ⁠ S ⊂ V {\displaystyle S\subset V} ⁠ is a vertex separator (or vertex cut, separating set) for nonadjacent vertices a...

of directed graphs, a graph is said to be strongly connected if every vertex is reachable from every other vertex. The strongly connected components of...

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 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...

the k-edge-connected Steiner network problem and the k-vertex-connected Steiner network problem, where the goal is to find a k-edge-connected graph or...

is just a vertex coloring of its line graph, and a face coloring of a plane graph is just a vertex coloring of its dual. However, non-vertex coloring problems...

object that is connected in pairs by edges. In the case of a directed graph, each edge has an orientation, from one vertex to another vertex. A path in a...

In mathematics, and, in particular, in graph theory, a rooted graph is a graph in which one vertex has been distinguished as the root. Both directed and...

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...

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...

and has odd vertex degrees, then L(G) is a vertex-transitive non-Cayley graph. If a graph G has an Euler cycle, that is, if G is connected and has an even...

called an odd cycle. A cycle graph is: 2-edge colorable, if and only if it has an even number of vertices 2-regular 2-vertex colorable, if and only if it...

Petersen graph. Only five connected vertex-transitive graphs with no Hamiltonian cycles are known: the complete graph K2, the Petersen graph, the Coxeter...

weighted directed graphs. The k-path partition problem is the problem of partitioning a given graph to a smallest collection of vertex-disjoint paths of...

triangle-free graphs are bowtie-free graphs, since every butterfly contains a triangle. In a k-vertex-connected graph, an edge is said to be k-contractible...

entire graph G is this version: A graph is k-vertex-connected (it has more than k vertices and it remains connected after removing fewer than k vertices)...

vertices in a k-vertex-connected graph there exists a cycle that passes through all the vertices in the set Gabriel Andrew Dirac (1925–1984), a graph theorist...

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 edges, often...

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...

Euler's Theorem: A connected graph has an Euler cycle if and only if every vertex has an even number of incident edges. The term Eulerian graph has two common...

a graph G = (V, E), a vertex labeling is a function of V to a set of labels; a graph with such a function defined is called a vertex-labeled graph. Likewise...

components of the graph. A graph is bipartite if and only if the spectrum of the graph is symmetric. In bipartite graphs, the size of minimum vertex cover is equal...

In graph theory, an expander graph is a sparse graph that has strong connectivity properties, quantified using vertex, edge or spectral expansion. Expander...

mathematical discipline of graph theory, a feedback vertex set (FVS) of a graph is a set of vertices whose removal leaves a graph without cycles ("removal"...