Просмотр кода страницы N-mesh

'''<math>n</math>-mesh''' --- <math>n</math>-сеть. 

An ''' <math>n</math>-dimensional mesh''' (abbreviated <math>n</math>-mesh) is the ''Cartesian product'' of <math>n</math> path graphs <math>P_{r_{1}}, \ldots, P_{r_{n}}</math>
of orders <math>r_{i}</math> and is denoted by <math>M(r_{1}, \ldots, r_{n})</math>. Thus,
<math>V(M) = \{(a_{1}, \ldots, a_{n})| \; (1 \leq a_{i} \leq r_{i})\}</math> and
for <math>x,y \in V(M)</math>, <math>(x,y) \in E(M)</math> if and only if

<math>\sum_{i=1}^{m} |x_{i} - y_{i}| = 1.</math>

A mesh <math>M(2,b)</math> is called a ''' ladder'''.

The ''' boundary''' of a 2-mesh <math>M(a,b)</math> is defined as the outer cycle
of <math>M(a,b)</math>, it has length <math>2a + 2b - 4</math> and is the cycle through the
vertices of degree 2 or 3 in <math>M(a,b)</math>. A submesh <math>M(c,d)</math> of the mesh
<math>M(a,b)</math> such that <math>c = a</math> or <math>b = d</math> is called a '''contraction''' of
<math>M(a,b)</math> and <math>M(a,b)</math> is said to be contracted to <math>M(c,d)</math>.