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4.1.1. Definition. A separating set or vertex cut of a graph G is a set S C V (G) such that G – S has more than one component. The connectivity of G, written «(G), is the minimum size of a vertex set S such that G – S is disconnected or has only one vertex. A graph G is k-connected if its connectivity is at least k. A graph other than a complete graph is k-connected if and only if every separating set has size at least k. We can view "k-connected" as a structural condition, while “connectivity k" is the solution of an optimization problem. Question What is K ( kn) and k ( km,n)

4.1.1. Definition. A separating set or vertex cut of a graph G is a set S C V (G) such that G – S has more than one component. The connectivity of G, written «(G), is the minimum size of a vertex set S such that G – S is disconnected or has only one vertex. A graph G is k-connected if its connectivity is at least k. A graph other than a complete graph is k-connected if and only if every separating set has size at least k. We can view "k-connected" as a structural condition, while “connectivity k" is the solution of an optimization problem. Question What is K ( kn) and k ( km,n)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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4.1.1. Definition. A separating set or vertex cut of a graph G is a set S C V(G) such that G – S has more than one component. The connectivity of G, written K(G), is the minimum size of a vertex set S such that G – S is disconnected or has only one vertex. A graph G is k-connected if its connectivity is at least k. A graph other than a complete graph is k-connected if and only if every separating set has size at least k. We can view “k-connected" as a structural condition, while “connectivity k" is the solution of an optimization problem. Question What is K ( kn) and k ( km,n)
Transcribed Image Text:4.1.1. Definition. A separating set or vertex cut of a graph G is a set S C V(G) such that G – S has more than one component. The connectivity of G, written K(G), is the minimum size of a vertex set S such that G – S is disconnected or has only one vertex. A graph G is k-connected if its connectivity is at least k. A graph other than a complete graph is k-connected if and only if every separating set has size at least k. We can view “k-connected" as a structural condition, while “connectivity k" is the solution of an optimization problem. Question What is K ( kn) and k ( km,n)
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