(a,b)-Linear class of graphs

[math]\displaystyle{ (a,b) }[/math]-Linear class of graphs --- [math]\displaystyle{ (a,b) }[/math]-линейный класс графов.

Given [math]\displaystyle{ a }[/math] and [math]\displaystyle{ b \in Q^{+} }[/math], we define the [math]\displaystyle{ (a,b) }[/math]-linear class, denoted by [math]\displaystyle{ L(a,b) }[/math], to be the set of all connected graphs such that [math]\displaystyle{ m = an - b }[/math]. The (1,1)-linear coclass coincides with the set of all trees and [math]\displaystyle{ L(1,0) }[/math] characterizes the set of connected graphs with only one cycle.