Graph bundle

Graph bundle --- связка графов.

Let [math]\displaystyle{ B }[/math] and [math]\displaystyle{ F }[/math] be graphs. A graph [math]\displaystyle{ G }[/math] is a (cartesian) graph bundle with fibre [math]\displaystyle{ F }[/math] over the base graph [math]\displaystyle{ B }[/math] if there is a mapping [math]\displaystyle{ p: \; G \rightarrow B }[/math] which satisfies the following conditions:

(1) it maps adjacent vertices of [math]\displaystyle{ G }[/math] to adjacent or identical vertices in [math]\displaystyle{ B }[/math],

(2) the edges are mapped to edges or collapsed to a vertex,

(3) for each vertex [math]\displaystyle{ v \in V(B) }[/math], [math]\displaystyle{ p^{-1}(v) \cong F }[/math], and for each edge [math]\displaystyle{ e \in E(B) }[/math], [math]\displaystyle{ p^{-1}(e) \cong K_{2} \Box F }[/math] ([math]\displaystyle{ \Box }[/math] denotes the cartesian product of graphs).