Codiameter

Codiameter --- кодиаметр.

Let [math]\displaystyle{ u,v \in V(G) }[/math] be any two distinct vertices. We denote by [math]\displaystyle{ p(u,v) }[/math] the length of the longest path connecting [math]\displaystyle{ u }[/math] and [math]\displaystyle{ v }[/math]. The codiameter of [math]\displaystyle{ G }[/math], denoted by [math]\displaystyle{ d^{\ast} }[/math], is defined to be [math]\displaystyle{ \min\{p(u,v) | \; u,v \in V(G)\} }[/math]. A graph [math]\displaystyle{ G }[/math] of order [math]\displaystyle{ n }[/math] is said to be Hamilton-connected if [math]\displaystyle{ d^{\ast}(G) = n-1 }[/math], i.e. every two distinct vertices are joined by a Hamiltonian path