Просмотр кода страницы K-Diameter

'''<math>k</math>-Diameter''' --- <math>k</math>-диаметр. 

Let <math>{\mathcal P}_{k}(u,v) = \{P_{1}, P_{2}, \cdots, P_{k}\}</math> be a family
of <math>k</math> vertex disjoint paths between <math>u</math> and <math>v</math> with lengths <math>|P_{1}|
\geq |P_{2}| \geq \cdots \geq |P_{k}|</math>. The '''<math>k</math>-distance''' between
<math>u</math> and <math>v</math> is the minimum <math>|P_{1}|</math> among all <math>{\mathcal P}_{k}(u,v)</math>,
and the '''<math>k</math>-diameter''' <math>d_{k}(G)</math> of <math>G</math> is

<math>d_{k}(G) = \max\{d_{k}(u,v): \; u \neq v\mbox{ and } u,v \in V(G).</math>

The concept of <math>k</math>-diameter naturally arises from the study of
routing, reliability, randomized routing, fault tolerance and other
communication protocols in the parallel architecture and distributed
computer networks.