Independent circuits

Independent circuits --- независимые циклы.

A set [math]\displaystyle{ {\mathcal C} }[/math] of circuits of [math]\displaystyle{ G }[/math] is called independent if for every nonempty subset [math]\displaystyle{ {\mathcal A} }[/math] of [math]\displaystyle{ {\mathcal C} }[/math] the symmetric difference of the circuits in [math]\displaystyle{ {\mathcal A} }[/math] is not empty. A maximal independent set of circuits of [math]\displaystyle{ G }[/math] is called a cycle basis of [math]\displaystyle{ G }[/math]. It is easy to see that every cycle basis of [math]\displaystyle{ G }[/math] has [math]\displaystyle{ |E(G)| - |V(G)| + c(G) }[/math] circuits, where [math]\displaystyle{ c(G) }[/math] is the number of components of [math]\displaystyle{ G }[/math].

See also

• Cyclomatic number.