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TitleThe graph based on Gr\"obner-Shirshov bases of groups.
Author(s) Firat Ates, I.Naci Cangul, A.Sinan cCevik, Eylem G. Karpuz
TypeArticle in Journal
AbstractLet us consider groups <a onClick="popup('http://www.fixedpointtheoryandapplications.com/content/2013/1/71/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.fixedpointtheoryandapplications.com/content/2013/1/71/mathml/M1">View MathML</a>, <a onClick="popup('http://www.fixedpointtheoryandapplications.com/content/2013/1/71/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.fixedpointtheoryandapplications.com/content/2013/1/71/mathml/M2">View MathML</a>, <a onClick="popup('http://www.fixedpointtheoryandapplications.com/content/2013/1/71/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.fixedpointtheoryandapplications.com/content/2013/1/71/mathml/M3">View MathML</a>, <a onClick="popup('http://www.fixedpointtheoryandapplications.com/content/2013/1/71/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://www.fixedpointtheoryandapplications.com/content/2013/1/71/mathml/M4">View MathML</a> and <a onClick="popup('http://www.fixedpointtheoryandapplications.com/content/2013/1/71/mathml/M5','MathML',630,470);return false;" target="_blank" href="http://www.fixedpointtheoryandapplications.com/content/2013/1/71/mathml/M5">View MathML</a>, where <a onClick="popup('http://www.fixedpointtheoryandapplications.com/content/2013/1/71/mathml/M6','MathML',630,470);return false;" target="_blank" href="http://www.fixedpointtheoryandapplications.com/content/2013/1/71/mathml/M6">View MathML</a>. In this paper, by defining a new graph <a onClick="popup('http://www.fixedpointtheoryandapplications.com/content/2013/1/71/mathml/M7','MathML',630,470);return false;" target="_blank" href="http://www.fixedpointtheoryandapplications.com/content/2013/1/71/mathml/M7">View MathML</a> based on the Gröbner-Shirshov bases over groups <a onClick="popup('http://www.fixedpointtheoryandapplications.com/content/2013/1/71/mathml/M8','MathML',630,470);return false;" target="_blank" href="http://www.fixedpointtheoryandapplications.com/content/2013/1/71/mathml/M8">View MathML</a>, where <a onClick="popup('http://www.fixedpointtheoryandapplications.com/content/2013/1/71/mathml/M9','MathML',630,470);return false;" target="_blank" href="http://www.fixedpointtheoryandapplications.com/content/2013/1/71/mathml/M9">View MathML</a>, we calculate the diameter, maximum and minimum degrees, girth, chromatic number, clique number, domination number, degree sequence and irregularity index of <a onClick="popup('http://www.fixedpointtheoryandapplications.com/content/2013/1/71/mathml/M7','MathML',630,470);return false;" target="_blank" href="http://www.fixedpointtheoryandapplications.com/content/2013/1/71/mathml/M7">View MathML</a>. Since graph theoretical studies (including such above graph parameters) consist of some fixed point techniques, they have been applied in such fields as chemistry (in the meaning of atoms, molecules, energy etc.) and engineering (in the meaning of signal processing etc.), game theory and physics. In addition, the Gröbner-Shirshov basis and the presentations of algebraic structures contain a mixture of algebra, topology and geometry within the purposes of this journal.
Keywordsgraphs; Gröbner-Shirshov bases; group presentation
ISSN1687-1812/e
URL http://www.fixedpointtheoryandapplications.com/content/2013/1/71
LanguageEnglish
JournalFixed Point Theory Appl.
Volume2013
Pages14
PublisherSpringer International Publishing (SpringerOpen), Cham
Year2013
Edition0
Translation No
Refereed No
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