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| {{Underlinked|date=August 2013}}
| | Hi there! :) My name is Oliver, I'm a student studying Nutritional Sciences from Frankenstein, Germany.<br><br>Here is my web-site ... [https://www.youtube.com/watch?v=NUCN0xd3iDc paket tour lombok 5 Hari 4 malam] |
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| The '''Bollobás–Riordan polynomial''' can mean a 3-variable polynomial invariant of graphs on orientable surfaces, or a more general 4-variable invariant of ribbon graphs, generalizing the [[Tutte polynomial]]. These polynomials were discovered by {{harvs |txt |author1-link=Béla Bollobás |last=Bollobás |author2-link=Oliver Riordan |last2=Riordan |year=2001 |year2=2002}}.
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| The 3-variable Bollobás–Riordan polynomial is given by
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| :<math>RG(x,y,z) =\sum_F x^{r(G)-r(F)}y^{n(F)}z^{k(F)-bc(F)+n(F)}</math>
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| where
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| * ''v''(''G'') is the number of vertices of ''G'';
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| * ''e''(''G'') is the number of its edges of ''G'';
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| * ''k''(''G'') is the number of components of ''G'';
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| * ''r''(''G'') is the rank of ''G'' such that ''r''(''G'') = ''v''(''G'') − ''k''(''G'');
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| * ''n''(''G'') is the nullity of such that ''n''(''G'') = ''e''(''G'') − ''r''(''G'');
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| * ''bc''(''G'') is the number of connected components of the boundary of ''G''.
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| ==References==
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| *{{Citation | last1=Bollobás | first1=Béla | author1-link=Béla Bollobás | last2=Riordan | first2=Oliver | title=A polynomial invariant of graphs on orientable surfaces | doi=10.1112/plms/83.3.513 | mr=1851080 | year=2001 | journal=Proceedings of the London Mathematical Society. Third Series | issn=0024-6115 | volume=83 | issue=3 | pages=513–531}}
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| *{{Citation | last1=Bollobás | first1=Béla | author1-link=Béla Bollobás | last2=Riordan | first2=Oliver | title=A polynomial of graphs on surfaces | doi=10.1007/s002080100297 | mr=1906909 | year=2002 | journal=[[Mathematische Annalen]] | issn=0025-5831 | volume=323 | issue=1 | pages=81–96}}
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| {{DEFAULTSORT:Bollobas-Riordan polynomial}}
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| [[Category:Polynomials]]
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Latest revision as of 20:27, 13 November 2014
Hi there! :) My name is Oliver, I'm a student studying Nutritional Sciences from Frankenstein, Germany.
Here is my web-site ... paket tour lombok 5 Hari 4 malam