Eccentricity of a vertex

Eccentricity of a vertex --- эксцентриситет вершины.

Let [math]\displaystyle{ d(x,y) }[/math] be the distance in a graph [math]\displaystyle{ G }[/math]. Then the eccentricity [math]\displaystyle{ e(v) }[/math] of a vertex [math]\displaystyle{ v }[/math] is the maximum over [math]\displaystyle{ d(v,x), \; x \in V(G) }[/math]. The minimum over the eccentricities of all vertices of [math]\displaystyle{ G }[/math] is the radius [math]\displaystyle{ rad(G) }[/math] of [math]\displaystyle{ G }[/math], whereas the maximum is the diameter [math]\displaystyle{ diam(G) }[/math] of [math]\displaystyle{ G }[/math]. A pair [math]\displaystyle{ x, y }[/math] of vertices of [math]\displaystyle{ G }[/math] is called diametral iff [math]\displaystyle{ d(x,y) = diam(G) }[/math]. A chain in [math]\displaystyle{ G }[/math] which length is equal to [math]\displaystyle{ diam(G) }[/math] is called a diametral chain.

See also

• Quasi-diameter, Quasi-radius.