Edge-superconnectivity: различия между версиями
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'''Edge-superconnectivity''' | '''Edge-superconnectivity''' — рёберная суперсвязность. | ||
Superconnectivity is a stronger measure of connectivity. A maximally | Superconnectivity is a stronger measure of connectivity. A maximally | ||
edge-connected graph is called '''super-<math>\lambda</math> | edge-connected graph is called '''super-<math>\lambda</math>''' if every edge cut | ||
<math>(C,\bar{C})</math> of cardinality <math>\delta(G)</math> satisfies either <math>|C| = | <math>(C,\bar{C})</math> of cardinality <math>\delta(G)</math> satisfies either <math>|C| = | ||
1</math> or <math>|\bar{C}| = 1</math>. In order to measure the super | 1</math> or <math>|\bar{C}| = 1</math>. In order to measure the super | ||
edge-connectivity, we use the following parameter: | edge-connectivity, we use the following parameter: | ||
<math>\lambda_{1}(G) = \min \{|(C,\bar{C})|, \; (C,\bar{C}) \mbox{ is a | <math>\lambda_{1}(G) = \min \{|(C,\bar{C})|, \; (C,\bar{C}) \mbox{ is a nontrivial edge cut}\}.</math> | ||
nontrivial edge cut}\}.</math> | |||
We define the '''edge-superconnectivity''' of a graph <math>G</math> as the value | We define the '''edge-superconnectivity''' of a graph <math>G</math> as the value | ||
of <math>\lambda_{1}(G)</math>. | of <math>\lambda_{1}(G)</math>. | ||
Текущая версия от 11:49, 13 апреля 2011
Edge-superconnectivity — рёберная суперсвязность.
Superconnectivity is a stronger measure of connectivity. A maximally edge-connected graph is called super-[math]\displaystyle{ \lambda }[/math] if every edge cut [math]\displaystyle{ (C,\bar{C}) }[/math] of cardinality [math]\displaystyle{ \delta(G) }[/math] satisfies either [math]\displaystyle{ |C| = 1 }[/math] or [math]\displaystyle{ |\bar{C}| = 1 }[/math]. In order to measure the super edge-connectivity, we use the following parameter:
[math]\displaystyle{ \lambda_{1}(G) = \min \{|(C,\bar{C})|, \; (C,\bar{C}) \mbox{ is a nontrivial edge cut}\}. }[/math]
We define the edge-superconnectivity of a graph [math]\displaystyle{ G }[/math] as the value of [math]\displaystyle{ \lambda_{1}(G) }[/math].