Amalgam: различия между версиями
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Glk (обсуждение | вклад) (Создана новая страница размером '''Amalgam''' --- амальгама. Given two plane trees <math>T_{1}</math> and <math>T_{2}</math>, with the same number of leaves an...) |
KEV (обсуждение | вклад) Нет описания правки |
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'''Amalgam''' | '''Amalgam''' — ''[[амальгама]].'' | ||
Given two plane trees <math>T_{1}</math> and <math>T_{2}</math>, | Given two plane [[tree|trees]] <math>\,T_{1}</math> and <math>\,T_{2}</math>, | ||
with the same number of leaves and without degree 2 | with the same number of [[leaf|leaves]] and without [[degree of a vertex|degree 2 vertices]], and a bijection <math>\varphi</math> between their | ||
vertices, and a bijection <math>\varphi</math> between their | |||
leaf sets which preserves their order on the plane. | leaf sets which preserves their order on the plane. | ||
The ''' amalgam''' <math>A = | The '''amalgam''' <math>A = | ||
{\mathcal A}(T_{1},T_{2}, \varphi)</math> is the union of the corresponding ''Halin graphs'' <math>{\mathcal H}(T_{1})</math> and <math>{\mathcal H}(T_{2})</math> in which the | {\mathcal A}(T_{1},T_{2}, \varphi)</math> is the union of the corresponding ''[[Halin graph|Halin graphs]]'' <math>{\mathcal H}(T_{1})</math> and <math>{\mathcal H}(T_{2})</math> in which the | ||
leaf vertices <math>v</math> and <math>\varphi(v)</math> are identified. | leaf vertices <math>\,v</math> and <math>\varphi(v)</math> are identified. | ||
Текущая версия от 12:42, 25 ноября 2011
Amalgam — амальгама.
Given two plane trees [math]\displaystyle{ \,T_{1} }[/math] and [math]\displaystyle{ \,T_{2} }[/math], with the same number of leaves and without degree 2 vertices, and a bijection [math]\displaystyle{ \varphi }[/math] between their leaf sets which preserves their order on the plane. The amalgam [math]\displaystyle{ A = {\mathcal A}(T_{1},T_{2}, \varphi) }[/math] is the union of the corresponding Halin graphs [math]\displaystyle{ {\mathcal H}(T_{1}) }[/math] and [math]\displaystyle{ {\mathcal H}(T_{2}) }[/math] in which the leaf vertices [math]\displaystyle{ \,v }[/math] and [math]\displaystyle{ \varphi(v) }[/math] are identified.