vertex-connected graph

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• K-vertex-connected graph — In graph theory, a graph G with vertex set V(G) is said to be k vertex connected (or k connected) if G setminus X is connected for all X subseteq V(G) with left| X ight| < k. In plain English, a graph is k connected if the graph remains connected …   Wikipedia

• K-edge-connected graph — In graph theory, a graph G with edge set E(G) is said to be k edge connected if G setminus X is connected for all X subseteq E(G) with left| X ight| < k. In plain English, a graph is k edge connected if the graph remains connected when you delete …   Wikipedia

• Graph (mathematics) — This article is about sets of vertices connected by edges. For graphs of mathematical functions, see Graph of a function. For statistical graphs, see Chart. Further information: Graph theory A drawing of a labeled graph on 6 vertices and 7 edges …   Wikipedia

• Vertex (graph theory) — For other uses, see Vertex (disambiguation). A graph with 6 vertices and 7 edges where the vertex number 6 on the far left is a leaf vertex or a pendant vertex In graph theory, a vertex (plural vertices) or node is the fundamental unit out of… …   Wikipedia

• Graph toughness — In graph theory, toughness is a measure of the connectivity of a graph. A graph G is said to be t tough if, for every k > 1, G cannot be split into k different connected components by the removal of fewer than tk vertices. For instance, a graph… …   Wikipedia

• graph theory — Math. the branch of mathematics dealing with linear graphs. [1965 70] * * * Mathematical theory of networks. A graph consists of nodes (also called points or vertices) and edges (lines) connecting certain pairs of nodes. An edge that connects a… …   Universalium

• Graph of groups — In geometric group theory, a graph of groups is an object consisting of a collection of groups indexed by the vertices and edges of a graph, together with a family of injective homomorphisms of the edge groups into the vertex groups.There is a… …   Wikipedia

• Connectivity (graph theory) — In 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) which need to be removed to disconnect the remaining nodes from each other[1]. It is… …   Wikipedia

• Degeneracy (graph theory) — In graph theory, a k degenerate graph is an undirected graph in which every subgraph has a vertex of degree at most k: that is, some vertex in the subgraph touches k or fewer of the subgraph s edges. The degeneracy of a graph is the smallest… …   Wikipedia

• Coxeter graph — This article is about the 3 regular graph. For the graph associated with a Coxeter group, see Coxeter diagram. Coxeter graph The Coxeter graph Vertices 28 Edges 42 …   Wikipedia

• Biconnected graph — In the mathematical discipline of graph theory, a biconnected graph is a connected graph with no articulation vertices.In other words, a biconnected graph is nonseparable, meaning if any vertex were to be removed, the graph will remain… …   Wikipedia