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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>.