Quasi-diameter

Quasi-diameter --- квазидиаметр.

Let [math]\displaystyle{ \rho(x,y) }[/math] be a distance function on the vertex set [math]\displaystyle{ V }[/math] of a directed graph without loops and let [math]\displaystyle{ \rho_{m}(x,y) }[/math] be a function defined by

[math]\displaystyle{ \rho_{m}(x,y) = \min\{\rho(x,y), \rho(y,x)\}. }[/math]

Then the quasi-diameter [math]\displaystyle{ d_{m}(G) = \max_{x,y \in V} \rho_{m}(x,y) }[/math] and the quasi-radius [math]\displaystyle{ r_{m}(G) = \min_{x \in V}\max_{y \in V}\rho_{m}(x,y) }[/math]