Slater number

Slater number --- число Слатера.

Let [math]\displaystyle{ G }[/math] be a connected graph with [math]\displaystyle{ n \geq 2 }[/math] vertices and let [math]\displaystyle{ v }[/math] be a vertex of [math]\displaystyle{ G }[/math]. The Slater number of a vertex [math]\displaystyle{ v }[/math], denoted by [math]\displaystyle{ f(v) }[/math], is

[math]\displaystyle{ f(v) = \min \{f(v,w): \; w \in V(G)\setminus \{v\}\}, }[/math]

where [math]\displaystyle{ f(v,w) }[/math] is the number of vertices of [math]\displaystyle{ G }[/math] that are closer to [math]\displaystyle{ v }[/math] than to [math]\displaystyle{ w }[/math] minus the number of vertices of [math]\displaystyle{ G }[/math] that are closer to [math]\displaystyle{ w }[/math] than to [math]\displaystyle{ v }[/math].