What does graph toughness mean?
Definitions for graph toughness
graph tough·ness
This dictionary definitions page includes all the possible meanings, example usage and translations of the word graph toughness.
Wiktionary
graph toughnessnoun
(mathematics) a measure, expressed by a positive integer (with the exception of complete graphs) of the connectivity of a graph
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 for a given real number t if, for every integer k > 1, G cannot be split into k different connected components by the removal of fewer than tk vertices. For instance, a graph is 1-tough if the number of components formed by removing a set of vertices is always at most as large as the number of removed vertices. The toughness of a graph is the maximum t for which it is t-tough; this is a finite number for all finite graphs except the complete graphs, which by convention have infinite toughness. Graph toughness was first introduced by Václav Chvátal (1973). Since then there has been extensive work by other mathematicians on toughness; the recent survey by Bauer, Broersma & Schmeichel (2006) lists 99 theorems and 162 papers on the subject.
Wikidata
Graph toughness
In graph theory, toughness is a measure of the connectivity of a graph. A graph G is said to be t-tough for a given real number t if, for every integer k > 1, G cannot be split into k different connected components by the removal of fewer than tk vertices. For instance, a graph is 1-tough if the number of components formed by removing a set of vertices is always at most as large as the number of removed vertices. The toughness of a graph is the maximum t for which it is t-tough; this is a finite number for all graphs except the complete graphs, which by convention have infinite toughness. Graph toughness was first introduced by Václav Chvátal . Since then there has been extensive work by other mathematicians on toughness; the recent survey by Bauer, Broersma & Schmiechel lists 99 theorems and 162 papers on the subject.
Numerology
Chaldean Numerology
The numerical value of graph toughness in Chaldean Numerology is: 6
Pythagorean Numerology
The numerical value of graph toughness in Pythagorean Numerology is: 7
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"graph toughness." Definitions.net. STANDS4 LLC, 2024. Web. 29 Apr. 2024. <https://www.definitions.net/definition/graph+toughness>.
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