Please use this identifier to cite or link to this item: http://hdl.handle.net/11452/33147
Title: The graph based on Grobner-Shirshov bases of groups
Authors: Karpuz, Eylem Güzel
Ateş, Fırat
Çevik, Ahmet Sinan
Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Anabilim Dalı.
0000-0002-0700-5774
0000-0002-0700-5774
Cangül, İsmail Naci
J-3505-2017
ABA-6206-2020
57189022403
Keywords: Graphs
Grobner-Shirshov bases
Group presentation
Zero-divisor graph
Inverse-semigroups
Cayley-graphs
Braid group
Ring
Extensions
Generators
Mathematics
Issue Date: 26-Mar-2013
Publisher: Springer
Citation: Karpuz, E. G. vd. (2013). “The graph based on Grobner-Shirshov bases of groups”. Fixed Point Theory and Applications, 2013.
Abstract: Let us consider groups G(1) = Z(k) * (Z(m) * Z(n)), G(2) = Z(k) x (Z(m) * Z(n)), G(3) = Z(k) * (Z(m) x Z(n)), G(4) = (Z(k) * Z(l)) * (Z(m) * Z(n)) and G(5) = (Z(k) * Z(l)) x (Z(m) * Z(n)), where k, l, m, n = 2. In this paper, by defining a new graph Gamma(G(i)) based on the Grobner-Shirshov bases over groups G(i), where 1 <= i <= 5, we calculate the diameter, maximum and minimum degrees, girth, chromatic number, clique number, domination number, degree sequence and irregularity index of Gamma(G(i)). 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 Grobner-Shirshov basis and the presentations of algebraic structures contain a mixture of algebra, topology and geometry within the purposes of this journal.
URI: https://doi.org/10.1186/1687-1812-2013-71
https://fixedpointtheoryandalgorithms.springeropen.com/articles/10.1186/1687-1812-2013-71
http://hdl.handle.net/11452/33147
ISSN: 1687-1812
Appears in Collections:Scopus
Web of Science

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