connected graph meaning
How do you know if a graph is k connected?
An equivalent definition is that a graph with at least two vertices is k -connected if, for every pair of its vertices, it is possible to find k vertex-independent paths connecting these vertices; see Menger's theorem ( Diestel 2005, p. 55). This definition produces the same answer, n − 1, for the connectivity of the complete graph Kn.
What are Connected Graphs? Graph Theory
What is a Component of a Graph? Connected Components Graph Theory
6.11 Connected Components How to find Connected Components in Graph Graph Theory
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Introduction to graph theory Definition of a graph
A component of G is a maximal connected subgraph (ie a connected subgraph with vertex set W for which no larger set Z containing W is connected) A graph |
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A theory of 3-connected graphs - CORE
A graph which is not n-separated is called (n+ I)-connected The 1-con- nected graphs are usually called simply the "connected graphs" We call G simple if it has |
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Minimally 3-Connected Graphs* - CORE
No such characterization has previously been available DEFINITION A k- connected graph G is minimally k-connected (mkc) if it has no |
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Minimally 3-Connected Graphs* - ScienceDirectcom
No such characterization has previously been available DEFINITION A k- connected graph G is minimally k-connected (mkc) if it has no |
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Chapter 5 Connectivity in graphs
We are going to study mostly 2-connected and rarely 3-connected graphs 5 1 Basic Definitions • A connected graph is an undirected graph that has a path |
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Graph Theory
Definition: A directed graph is weakly connected if there is a path between every two vertices in the underlying undirected graph, which is the undirected graph |
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Chapter 5 Connectivity
By definition, being 1-connected, 1-edge-connected or connected is equivalent Similarly, adding a new vertex of degree k to a k-edge-connected graph yields |
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K-Connectivity
Definition: G is k-connected if • V(G) > k, and • Removing fewer than k vertices does not disconnect the graph (We will say that every graph is 0-connected ) |
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Graph Theory
Definition 5 7 Let G be a graph A maximal connected subgraph of G without a cut vertex is called a block block |
