Decay number

Decay number --- число распада.

Given a connected graph [math]\displaystyle{ G }[/math], the decay number [math]\displaystyle{ \zeta(G) }[/math] is the smallest number of components a cotree of [math]\displaystyle{ G }[/math] can have. That is

[math]\displaystyle{ \zeta(G) = \min\{c(G - E(T))| \; T \mbox{ is a spanning tree of } G\}, }[/math]

where [math]\displaystyle{ c(H) }[/math] denotes the number of connected components of a graph [math]\displaystyle{ H }[/math].