Crown of graphs: различия между версиями

Материал из WEGA
Перейти к навигации Перейти к поиску
(Новая страница: «'''Crown of graphs''' --- корона графов. For positive integers <math>k \leq n</math>, the '''crown of graphs''' <math>C_{n,k}</math> is a graph with a …»)
 
Нет описания правки
 
Строка 1: Строка 1:
'''Crown of graphs''' --- корона графов.  
'''Crown of graphs''' — ''[[корона графов]].''
 
For positive integers <math>k \leq n</math>, the '''crown of graphs''' <math>C_{n,k}</math> is a [[graph, undirected graph, nonoriented graph|graph]] with a [[vertex]] set <math>\{a_{1}, \ldots, a_{n}, b_{1}, \ldots, b_{n}\}</math> and an [[edge]] set <math>\{a_{i}b_{j}: \; 1 \leq i \leq n, j = i+1, i+2, \ldots,i+k\pmod{n}\}</math>. For any positive integer <math>\lambda</math>, let <math>\lambda C_{n,k}</math> denote a multiple graph obtained from the crown <math>C_{n,k}</math> by replacing each edge <math>e</math> by <math>\lambda</math> edges with the same end vertices
as those of <math>e</math>. We call <math>\lambda C_{n,k}</math> a '''[[multicrown]]'''.


For positive integers <math>k \leq n</math>, the '''crown of graphs''' <math>C_{n,k}</math> is a
graph with a vertex set <math>\{a_{1}, \ldots, a_{n}, b_{1}, \ldots, b_{n}\}</math>
and an edge set <math>\{a_{i}b_{j}: \; 1 \leq i \leq n, j = i+1, i+2, \ldots,
i+k\pmod{n}\}</math>. For any positive integer <math>\lambda</math>, let <math>\lambda
C_{n,k}</math> denote a multiple graph obtained from the crown <math>C_{n,k}</math> by
replacing each edge <math>e</math> by <math>\lambda</math> edges with the same end vertices
as those of <math>e</math>. We call <math>\lambda C_{n,k}</math> a '''multicrown'''.
==See also==
==See also==
*''Corona''.
 
* ''[[Corona]]''.
 
==Литература==
 
* Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.

Текущая версия от 16:03, 25 декабря 2018

Crown of graphs — корона графов.

For positive integers [math]\displaystyle{ k \leq n }[/math], the crown of graphs [math]\displaystyle{ C_{n,k} }[/math] is a graph with a vertex set [math]\displaystyle{ \{a_{1}, \ldots, a_{n}, b_{1}, \ldots, b_{n}\} }[/math] and an edge set [math]\displaystyle{ \{a_{i}b_{j}: \; 1 \leq i \leq n, j = i+1, i+2, \ldots,i+k\pmod{n}\} }[/math]. For any positive integer [math]\displaystyle{ \lambda }[/math], let [math]\displaystyle{ \lambda C_{n,k} }[/math] denote a multiple graph obtained from the crown [math]\displaystyle{ C_{n,k} }[/math] by replacing each edge [math]\displaystyle{ e }[/math] by [math]\displaystyle{ \lambda }[/math] edges with the same end vertices as those of [math]\displaystyle{ e }[/math]. We call [math]\displaystyle{ \lambda C_{n,k} }[/math] a multicrown.

See also

Литература

  • Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.
Источник — http://pco.iis.nsk.su/wega/index.php?title=Crown_of_graphs&oldid=13671