P-Radius

[math]\displaystyle{ p }[/math]-Radius --- [math]\displaystyle{ p }[/math]-радиус.

Let [math]\displaystyle{ G = (V,E) }[/math] be a graph and [math]\displaystyle{ w: \; V \rightarrow R^{+} \cup \{0\} }[/math] be a nonnegative weight function defined on [math]\displaystyle{ V }[/math]. We define the radius [math]\displaystyle{ r(S) }[/math] of a set [math]\displaystyle{ S \subseteq V }[/math] as [math]\displaystyle{ \max\{w(u)d(u,S): \; u \in V\} }[/math], where [math]\displaystyle{ d(u,S) = \min\{d(u,v): \; v |in S\} }[/math]. For a given positive integer [math]\displaystyle{ p \leq |V| }[/math], we define the [math]\displaystyle{ p }[/math]-radius of [math]\displaystyle{ G }[/math] as

[math]\displaystyle{ r_{p}(G) = \min \{r(C); \; C \subseteq V, \; |C| = p\}. }[/math]

See also

• Radius of a graph, [math]\displaystyle{ p }[/math]-center.