Proofs of convergence of random variables: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older edit
en>ChrisGualtieri
en>Jonesey95
 
Line 1: Line 1:
{{infobox graph
Produce a assessment GHD Hair Straighteners Particular Offers Important sil. Compose a review Hair Straighteners Dropshipping Luxury GHD DarkUS$. Produce a review International Model Days Return Cherished silve. The heat tiles are designed from clean ceramic and less costly chips designed of diverse supplies and rectifiers are only engrossed in ceramic or ceramic drained. Help you save: % off Ghd Gold Typical Styler$. The reward of ceramic tiles is that it is scorching, thicker hair Colour of GHD Cherished Reward Established is traditional, so Nostalgic ghd MK Purple Styler ghd MK Purple Styler Excellent for extended, thicker hair GHD purple Straightener in no way appear to be to fall short to be sure to wit GHD Radiance Gift Established GHD Radiance Reward Established ghd's most sought following styler The ghd new zealand Styler Radiance Established Limited Edition co ghd MK Dark Styler ghd MK Darkish Styler Great for extended, This styling rod is controlled alongside a tiny processor which enhances the protection of the system.
| name = Friendship graph
| image = [[Image: Friendship graph 8.svg|120px]]
| image_caption = The friendship graph ''F''<sub>8</sub>.
| vertices = ''2n+1''
| edges = ''3n''
| automorphisms    =
| chromatic_number = 3
| girth = 3
| diameter = 2
| radius = 1
| chromatic_index = ''2n''
|notation = ''F<sub>n</sub>''
| properties = [[Unit distance graph|Unit distance]]<br>[[planar graph|Planar]]<br>[[Eulerian graph|Eulerian]]<br>[[Factor-critical graph|factor-critical]]
}}
[[Image:Friendship graphs.svg|thumb|450px|The friendship graphs ''F''<sub>2</sub>, ''F''<sub>3</sub> and ''F''<sub>4</sub>.]]
In the [[mathematics|mathematical]] field of [[graph theory]], the '''friendship graph''' (or '''Dutch windmill graph''' or '''''n''-fan''') ''F''<sub>''n''</sub> is a [[planar graph|planar]] [[undirected graph]] with ''2n+1'' vertices and ''3n'' edges.<ref>{{MathWorld|urlname=DutchWindmillGraph|title=Dutch Windmill Graph}}</ref>


The friendship graph ''F<sub>n</sub>'' can be constructed by joining ''n'' copies of the [[cycle graph]] ''C''<sub>3</sub> with a common vertex.<ref>Gallian, J. A. "Dynamic Survey DS6: Graph Labeling." Electronic J. Combinatorics, DS6, 1-58, Jan. 3, 2007. [http://www.combinatorics.org/Surveys/ds6.pdf].</ref>
Just by making use of a top high-quality Excellent hair days hair straightening iron, you can aquire a great and amazing glimpse. With a number of beneficial options it has come to be the to start with preference for the fashion aficionados. The new improved technological know-how aims at straightening your hair with no damaging. With an impressive solution with GHD MK you are undoubtedly to get the several years of styling enjoyment and also can make a fashion assertion of your individual.


By construction, the friendship graph ''F<sub>n</sub>'' is isomorphic to the [[windmill graph]] Wd(3,''n''). It is [[Unit distance graph|unit distance]] with girth 3, diameter 2 and radius 1. The graph ''F''<sub>2</sub> is isomorphic to the [[butterfly graph]].
Choose a damp piece of cloth and rub it on the plates of hair straightener which these are very little heat not a great deal incredibly hot as it may burn off your hand. This very styling products has grown to the rank of the most typically made use of hair styler. You can some leaning spray on the plates to remove the residues. which can be all I &#. June th, Acquiring the Excellent Straightener As a substitute of throwing excellent income just after lousy as is usually the scenario if you buy low-priced hair straightners from the retailer, Just just take a glance at some of the GHD hair straightener assessments and you may see that the vast the greater part of people are very pleased with GHD hair straighteners.


==Friendship theorem==
So why do persons like,ghd iv mini styler so much. God understands, you dont want to mail these telephones any personal for that reason make good that they are a qualified PAT certified fixes company, most of these will likely be ideal VAT stated organizations. When implementing GHD's of equivalent bigger warmth hair straighteners you have to phase strands of hair with sectioning clips and spray a liberal quantities of the heat security spray on just about each individual space in advance of styling.
The '''friendship theorem''' of {{harvs|first1=Paul|last1=Erdős|author1-link=Paul Erdős|first2=Alfréd|last2=Rényi|author2-link=Alfréd Rényi|first3=Vera T.|last3=Sós|author3-link=Vera T. Sós|year=1966|txt}}<ref>{{citation|first1=Paul|last1=Erdős|author1-link=Paul Erdős|first2=Alfréd|last2=Rényi|author2-link=Alfréd Rényi|first3=Vera T.|last3=Sós|author3-link=Vera T. Sós|url=http://www.renyi.hu/~p_erdos/1966-06.pdf|title=On a problem of graph theory|journal=Studia Sci. Math. Hungar.|volume=1|year=1966|pages=215–235}}.</ref> states that the finite graphs with the property that every two vertices have exactly one neighbor in common are exactly the friendship graphs. Informally, if a group of people has the property that every pair of people has exactly a friend in common, then there must be one person who is a friend to all the others. However, for infinite graphs, there can be many different graphs with the same cardinality that have this property.<ref>{{citation|first1=Václav|last1=Chvátal|author1-link=Václav Chvátal|first2=Anton|last2=Kotzig|first3=Ivo G.|last3=Rosenberg|first4=Roy O.|last4=Davies|title=There are <math>\scriptstyle 2^{\aleph_\alpha}</math> friendship graphs of cardinal <math>\scriptstyle\aleph_\alpha</math>|journal=Canadian Mathematical Bulletin|volume=19|issue=4|year=1976|pages=431–433}}. </ref> A combinatorial proof was given by Mertzios and Unger. <ref>{{cite journal|last=Mertzios|first=George|coauthors=Walter Unger|title=The friendship problem on graphs|journal=Relations, Orders and Graphs: Interaction with Computer Science|date=2008|url=http://www.dur.ac.uk/george.mertzios/papers/Conf/Conf_Windmills.pdf}}</ref> Another proof was given by Craig Huneke <ref>Huneke, Craig. [http://www.jstor.org/discover/10.2307/2695332?uid=3739832&uid=2&uid=4&uid=3739256&sid=21102015693863 "The Friendship Theorem."] The American Mathematical Monthly 109.2 (2002): 192-94. JSTOR. Mathematical Association of America. Web. <http://www.jstor.org/discover/10.2307/2695332?uid=3739832&uid=2129&uid=2&uid=70&uid=4&uid=3739256&sid=21102213900737></ref>


Bear in intellect GHD hair straighteners heat up to a remarkable temperature of about levels c so make self-confident you use a shielding spray with a suitable resistance to keep absent from damage to your hair.<br><br>


==Labeling and colouring==
If you loved this short article and you want to receive more information regarding [http://tinyurl.com/mdm2hs2 http://tinyurl.com/mdm2hs2] i implore you to visit our own web site.
The friendship graph has [[chromatic number]] 3 and [[chromatic index]] ''2n''. Its [[chromatic polynomial]] can be deduced from the chromatic polynomial of the cycle graph ''C''<sub>3</sub> and is equal to <math>(x-2)^n (x-1)^n x</math>.
 
The friendship graph ''F<sub>n</sub>'' is [[Edge-graceful labeling|edge-graceful]] if and only if ''n'' is odd. It is [[Graceful labeling|graceful]] if and only if ''n'' ≡ 0 (mod 4) or ''n'' ≡ 1 (mod 4).<ref>J.C. Bermond, A. E. Brouwer, and A. Germa, "Systèmes de triplets et différences associées", Problèmes Combinatoires et Théorie des Graphes, Colloq. Intern. du CNRS, 260, Editions du Centre Nationale de la Recherche Scientifique, Paris (1978) 35-38.</ref><ref>J. C. Bermond, A. Kotzig, and J. Turgeon, On a combinatorial problem of antennas in radioastronomy, in Combinatorics, A. Hajnal and V. T. Sos, eds., Colloq. Math. Soc. János Bolyai, 18, 2 vols. North-Holland, Amsterdam (1978) 135-149.</ref>
 
Every friendship graph is [[Factor-critical graph|factor-critical]].
 
==Extremal graph theory==
According to [[extremal graph theory]], every graph with sufficiently many edges (relative to its number of vertices) must contain a ''k''-fan. More specifically, this is true for an ''n''-vertex graph if the number of edges is
:<math>\left\lfloor \frac{n^2}{4}\right\rfloor + f(k),</math>
where ''f''(''k'') is ''k''<sup>2</sup>&nbsp;&minus;&nbsp;''k'' if ''k'' is odd, and
''f''(''k'') is ''k''<sup>2</sup>&nbsp;&minus;&nbsp;3''k''/2 if ''k'' is even. These bounds generalize [[Turán's theorem]] on the number of edges in a [[triangle-free graph]], and they are the best possible bounds for this problem, in that for any smaller number of edges there exist graphs that do not contain a ''k''-fan.<ref>{{citation
| last1 = Erdős | first1 = P. | author1-link = Paul Erdős
| last2 = Füredi | first2 = Z. | author2-link = Zoltán Füredi
| last3 = Gould | first3 = R. J. | author3-link = Ronald J. Gould
| last4 = Gunderson | first4 = D. S. | author4-link = David Shane Gunderson
| doi = 10.1006/jctb.1995.1026
| issue = 1
| journal = Journal of Combinatorial Theory
| mr = 1328293
| pages = 89–100
| series = Series B
| title = Extremal graphs for intersecting triangles
| url = http://www.math.uiuc.edu/~z-furedi/PUBS/furedi_erdos_gould_gunderson_triangles.ps
| volume = 64
| year = 1995}}.</ref>
 
== References ==
{{reflist}}
 
[[Category:Parametric families of graphs]]
[[Category:Planar graphs]]

Latest revision as of 03:48, 14 September 2014

Produce a assessment GHD Hair Straighteners Particular Offers Important sil. Compose a review Hair Straighteners Dropshipping Luxury GHD DarkUS$. Produce a review International Model Days Return Cherished silve. The heat tiles are designed from clean ceramic and less costly chips designed of diverse supplies and rectifiers are only engrossed in ceramic or ceramic drained. Help you save: % off Ghd Gold Typical Styler$. The reward of ceramic tiles is that it is scorching, thicker hair Colour of GHD Cherished Reward Established is traditional, so Nostalgic ghd MK Purple Styler ghd MK Purple Styler Excellent for extended, thicker hair GHD purple Straightener in no way appear to be to fall short to be sure to wit GHD Radiance Gift Established GHD Radiance Reward Established ghd's most sought following styler The ghd new zealand Styler Radiance Established Limited Edition co ghd MK Dark Styler ghd MK Darkish Styler Great for extended, This styling rod is controlled alongside a tiny processor which enhances the protection of the system. 

Just by making use of a top high-quality Excellent hair days hair straightening iron, you can aquire a great and amazing glimpse. With a number of beneficial options it has come to be the to start with preference for the fashion aficionados. The new improved technological know-how aims at straightening your hair with no damaging. With an impressive solution with GHD MK you are undoubtedly to get the several years of styling enjoyment and also can make a fashion assertion of your individual.

Choose a damp piece of cloth and rub it on the plates of hair straightener which these are very little heat not a great deal incredibly hot as it may burn off your hand. This very styling products has grown to the rank of the most typically made use of hair styler. You can some leaning spray on the plates to remove the residues. which can be all I &#. June th, Acquiring the Excellent Straightener As a substitute of throwing excellent income just after lousy as is usually the scenario if you buy low-priced hair straightners from the retailer, Just just take a glance at some of the GHD hair straightener assessments and you may see that the vast the greater part of people are very pleased with GHD hair straighteners.

So why do persons like,ghd iv mini styler so much. God understands, you dont want to mail these telephones any personal for that reason make good that they are a qualified PAT certified fixes company, most of these will likely be ideal VAT stated organizations. When implementing GHD's of equivalent bigger warmth hair straighteners you have to phase strands of hair with sectioning clips and spray a liberal quantities of the heat security spray on just about each individual space in advance of styling.

Bear in intellect GHD hair straighteners heat up to a remarkable temperature of about levels c so make self-confident you use a shielding spray with a suitable resistance to keep absent from damage to your hair.

If you loved this short article and you want to receive more information regarding http://tinyurl.com/mdm2hs2 i implore you to visit our own web site.

Retrieved from "https://en.formulasearchengine.com/index.php?title=Proofs_of_convergence_of_random_variables&oldid=265102"