Graph, undirected graph, nonoriented graph

Graph, undirected graph, nonoriented graph --- граф, неориентированный граф.

A graph consists of a finite set of vertices or nodes [math]\displaystyle{ V }[/math], a finite set of edges [math]\displaystyle{ E }[/math], and a mapping [math]\displaystyle{ Ends }[/math] from [math]\displaystyle{ E }[/math] to [math]\displaystyle{ V \times V }[/math] assigning to each edge [math]\displaystyle{ e }[/math] two, not necessarily distinct, vertices of [math]\displaystyle{ V }[/math] (the extremities of [math]\displaystyle{ e }[/math]). The graph [math]\displaystyle{ G }[/math] will be denoted by [math]\displaystyle{ G = (V, E, Ends) }[/math] or simply [math]\displaystyle{ G = (V, E) }[/math]. It is easy to see that an edge [math]\displaystyle{ e = (v,w) }[/math] corresponds to an undirected pair [math]\displaystyle{ (v,w) }[/math] of vertices. If we consider ordered pairs of vertices [math]\displaystyle{ (v,w) }[/math], we say about a directed graph with the set of arcs [math]\displaystyle{ A = \{(v,w)\} }[/math].