Codiameter: различия между версиями

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'''Codiameter''' --- кодиаметр.  
'''Codiameter''' — ''[[кодиаметр]].''


Let <math>u,v \in V(G)</math> be any two distinct vertices. We denote by <math>p(u,v)</math>
Let <math>\,u,v \in V(G)</math> be any two distinct [[vertex|vertices]]. We denote by <math>\,p(u,v)</math> the length of the longest [[path]] connecting <math>\,u</math> and <math>\,v</math>. The '''codiameter''' of <math>\,G</math>, denoted by <math>\,d^{\ast}</math>, is defined to be
the length of the longest path connecting <math>u</math> and <math>v</math>. The '''codiameter''' of <math>G</math>, denoted by <math>d^{\ast}</math>, is defined to be
<math>\min\{p(u,v) | \; u,v \in V(G)\}</math>. A [[graph, undirected graph, nonoriented graph|graph]] <math>\,G</math> of order <math>\,n</math> is said to be '''[[Hamiltonian connected graph|Hamilton-connected]]''' if <math>d^{\ast}(G) = n-1</math>, i.e. every two distinct vertices are joined by a ''[[Hamiltonian path]]''
<math>\min\{p(u,v) | \; u,v \in V(G)\}</math>. A graph <math>G</math> of order <math>n</math> is said
 
to be '''Hamilton-connected''' if <math>d^{\ast}(G) = n-1</math>, i.e. every two
==Литература==
distinct vertices are joined by a ''Hamiltonian path''
 
* Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.

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