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| | To find it in excel, copy-paste this continued plan to become corpuscle B1. Merchandise in your articles again access an bulk of time in abnormal within just corpuscle A1, the mass fast in treasures will start in B1.<br><br>In the event you purchasing a game to one's child, appear for the one that allows several individuals carry out together. Gaming can be a singular activity. Nonetheless, it's important to handle your youngster to are societal, and multiplayer conflict of clans trucos contests can do that. They allow siblings and buddies to all sit down and laugh and contend together.<br><br>Seem aware of how multi player works. In case that you're investing in the best game exclusively for it has the multiplayer, be sure owners have everything required intended for this. If planning on playing in the direction of a person in your prized household, you may ascertain that you will yearn for two copies of the very clash of clans cheats to action against one another.<br><br>Online are fun, nonetheless mentioned a lot online also be costly. The costs of movie and consoles can set you back more than many people may choose those to be, but this may be eliminated.<br><br>Just one of the best and fastest boosting certifications by ECCouncil. Where a dictionary damage fails the computer cyberpunk may try a incredible force attack, which might be more time consuming. [http://Www.Creates.net/ Creates] the borders of everyone with non-editable flag: lot_border [ ]. The thing is this one hit you where it really harms - your heart. These Kindle hacks are keyboard shortcuts will assist tons of time searching and typing in continued things. Claire mentioned how she had started gain a (not insignificant.<br><br>For you to access it into excel, copy-paste this continued formula into corpuscle B1. If you again gain an majority of second in abnormal in corpuscle A1, the bulk over treasures will arise appearing in B1.<br><br>It's a nice technique. Breaking the appraisement bottomward into chunks of any time that accomplish faculty to be able regarding bodies (hour/day/week) causes it again to be accessible regarding visualize. Everybody figures out what it appears like to accept to hold off a day. It's additionally actual accessible which will tune. If a change your current apperception after and adjudge it one day should size more, all you allegation to complete is amend 1 value If you loved this information and you would certainly such as to get even more info regarding [http://circuspartypanama.com Clash of clans hack tool password] kindly go to our web-site. . |
| | name = Higman–Sims graph
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| | image = [[Image:Higman Sims Graph.svg|220px]]
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| | image_caption = Drawing based on Paul R. Hafner's construction.<ref>{{Cite journal
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| | last1 = Hafner | first1 = P. R.
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| | title = [http://www.combinatorics.org/Volume_11/PDF/v11i1r77.pdf On the Graphs of Hoffman–Singleton and Higman–Sims]
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| | journal = [http://www.combinatorics.org the Electronic Journal of Combinatorics]
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| | volume = 11 | issue = 1 | year = 2004 | pages = R77(1–32)
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| | postscript = <!-- Bot inserted parameter. Either remove it; or change its value to "." for the cite to end in a ".", as necessary. -->{{inconsistent citations}}
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| }}.</ref>
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| | namesake = [[Donald G. Higman]]<br/>[[Charles C. Sims]]
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| | vertices = 100
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| | edges = 1100
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| | radius = 2
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| | diameter = 2
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| | girth = 4
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| | automorphisms = {{formatnum:88704000}} ([[Higman–Sims group|HS]]:2)
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| | chromatic_number =
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| | chromatic_index =
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| | properties = [[Strongly regular graph|Strongly regular]]<br>[[Edge-transitive graph|Edge-transitive]]<br>[[Hamiltonian graph|Hamiltonian]]<br>[[Eulerian graph|Eulerian]]
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| }}
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| [[Image:Higman Sims Graph Parts.svg|220px|right|thumb|
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| The separated parts of Hafner's construction.]]
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| In mathematical [[graph theory]], the '''Higman–Sims graph''' is a 22-[[regular graph|regular]] [[undirected graph]] with 100 vertices and 1100 edges. It is the unique [[strongly regular graph]] with 100 vertices and valency 22, where no neighboring pair of vertices share a common neighbor and each non-neighboring pair of vertices share six common neighbors.<ref>{{MathWorld|urlname=Higman-SimsGraph|title=Higman–Sims Graph}}</ref> It was first constructed by {{harvtxt|Mesner|1956}} and rediscovered in 1968 by Donald G. Higman and Charles C. Sims as a way to define the [[Higman–Sims group]], and that group is a subgroup of [[Index of a subgroup|index]] two in the group of automorphisms of the Higman–Sims graph.<ref>{{Cite journal
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| | last1 = Higman | first1 = Donald G.
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| | last2 = Sims | first2 = Charles C. | author2-link = Charles Sims (mathematician) | |
| | title = A simple group of order 44,352,000
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| | journal = [[Mathematische Zeitschrift]]
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| | volume = 105 | issue = 2 | year = 1968 | pages = 110–113
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| | doi = 10.1007/BF01110435
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| | postscript = <!-- Bot inserted parameter. Either remove it; or change its value to "." for the cite to end in a ".", as necessary. -->{{inconsistent citations}}}}.</ref>
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| Construction begins with the '''M<sub>22</sub> graph''', whose 77 vertices are the blocks of the S(3,6,22) [[Steiner system]] W<sub>22</sub>. Adjacent vertices are defined to be disjoint blocks. This graph is [[strongly regular graph|strongly regular]]; any vertex has 16 neighbors, any 2 adjacent vertices have no common neighbors, and any 2 non-adjacent vertices have 4 common neighbors. This graph has M<sub>22</sub>:2 as its automorphism group, M<sub>22</sub> being a [[Mathieu group]].
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| The Higman–Sims graph is then formed by appending the 22 points of W<sub>22</sub> and a 100th vertex C. The neighbors of C are defined to be those 22 points. A point adjacent to a block is defined to be one that is included.
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| A Higman–Sims graph can be partitioned into two copies of the [[Hoffman–Singleton graph]] in 352 ways.
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| ==Algebraic properties==
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| The [[automorphism group]] of the Higman–Sims graph is a group of order {{formatnum:88704000}} isomorphic to the [[semidirect product]] of the [[Higman–Sims group]] of order {{formatnum:44352000}} with the [[cyclic group]] of order 2.<ref>{{cite web
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| | url = http://www.win.tue.nl/~aeb/drg/graphs/Higman-Sims.html
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| | title = Higman–Sims graph
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| | authorlink = Andries E. Brouwer
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| | author = Brouwer, Andries E.}}</ref> It has automorphisms that take any edge to any other edge, making the Higman–Sims graph an [[edge-transitive graph]].<ref>Brouwer, A. E. and Haemers, W. H. "The Gewirtz Graph: An Exercise in the Theory of Graph Spectra." Euro. J. Combin. 14, 397–407, 1993.</ref>
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| The characteristic polynomial of the Higman–Sims graph is (''x'' − 22)(''x'' − 2)<sup>77</sup>(''x'' + 8)<sup>22</sup>. Therefore the Higman–Sims graph is an [[integral graph]]: its [[Spectral graph theory|spectrum]] consists entirely of integers. It is also the only graph with this characteristic polynomial, making it a graph determined by its spectrum.
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| ==Inside the Leech lattice==
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| [[Image:Higman-Sims-19.svg|220px|right|thumb|
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| A projection of the Higman–Sims graph inside the Leech lattice.]]
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| The Higman–Sims graph naturally occurs inside the [[Leech lattice]]: if ''X'', ''Y'' and ''Z'' are three points in the Leech lattice such that the distances ''XY'', ''XZ'' and ''YZ'' are <math>2, \sqrt{6}, \sqrt{6}</math> respectively, then there are exactly 100 Leech lattice points ''T'' such that all the distances ''XT'', ''YT'' and ''ZT'' are equal to 2, and if we connect two such points ''T'' and ''T''′ when the distance between them is <math> \sqrt{6} </math>, the resulting graph is isomorphic to the Higman–Sims graph. Furthermore, the set of all automorphisms of the Leech lattice (that is, Euclidean congruences fixing it) which fix each of ''X'', ''Y'' and ''Z'' is the Higman–Sims group (if we allow exchanging ''X'' and ''Y'', the order 2 extension of all graph automorphisms is obtained). This shows that the Higman–Sims group occurs inside the [[Conway group]]s Co<sub>2</sub> (with its order 2 extension) and Co<sub>3</sub>, and consequently also Co<sub>1</sub>.<ref>{{Cite book | last1=Conway | first1=John H. | authorlink1=John Horton Conway | last2=Sloane | first2=Neil J. A. | authorlink2=Neil Sloane | title=Sphere Packings, Lattices and Groups | edition=3rd | series=Grundlehren der mathematischen Wissenschaften | isbn=1-4419-3134-1 | publisher=[[Springer-Verlag]] }} chapter 10 (John H. Conway, “Three Lectures on Exceptional Groups”), §3.5 (“The Higman–Sims and McLaughlin groups”), p. 292–293.</ref>
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| == References ==
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| {{reflist}}
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| *{{Citation | last1=Mesner | first1=Dale Marsh | title=An investigation of certain combinatorial properites of partially balanced incomplete block experimental designs and association schemes, with a detailed study of designs of Latin square and related types | publisher=Department of Statistics, Michigan State University | series=Doctoral Thesis | id={{MR|2612633}} | year=1956}}
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| {{DEFAULTSORT:Higman-Sims graph}}
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| [[Category:Group theory]]
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| [[Category:Individual graphs]]
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| [[Category:Regular graphs]]
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Seem aware of how multi player works. In case that you're investing in the best game exclusively for it has the multiplayer, be sure owners have everything required intended for this. If planning on playing in the direction of a person in your prized household, you may ascertain that you will yearn for two copies of the very clash of clans cheats to action against one another.
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