Просмотр кода страницы Pseudo-product

'''Pseudo-product''' --- псевдопроизведение. 

Let <math>G</math> and <math>G'</math> be simple graphs on the same set of vertices <math>V(G) =
V(G') = V</math>, where <math>|V| = n \geq 1</math>. Define the ''' pseudo product''' of
<math>G</math> and <math>G'</math> to be the simple graph <math>G * G'</math> on the vertex set <math>V</math>
with the edge set <math>E(G * G') = E(G) \cup E(G') \cup E^{\ast}</math>, where

<math>E^{\ast} = \{\{u,v\}: \; \exists w \in V: \; \{u,w\} \in E(G),
\{w,v\} \in E(G'),</math>
<math>\mbox{ and }\exists w' \in V: \; \{u,w'\} \in E(G'), \{w',v\}
\in E(G)\}.</math>

For a simple graph <math>G</math> and nonnegative integers <math>s</math> and <math>t</math>, we have

<math>G^{s} * G^{t} = G^{s+t}.</math>

In particular, the pseudo product is an associative operation on the
set <math>\{G^{k}: \; k \in \{0,1,2, \ldots,\}\}</math> for any fixed simple
graph <math>G</math>.