Edge-superconnectivity: различия между версиями

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'''Edge-superconnectivity''' --- рёберная суперсвязность.  
'''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>} if every edge cut
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].