The graph based on Grobner-Shirshov bases of groups

GÜZEL KARPUZ E., ATEŞ F., ÇEVİK A. S., CANGÜL İ. N.

FIXED POINT THEORY AND APPLICATIONS, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası:
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1186/1687-1812-2013-71
  • Dergi Adı: FIXED POINT THEORY AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: graphs, Grobner-Shirshov bases, group presentation, ZERO-DIVISOR GRAPH, INVERSE-SEMIGROUPS, CAYLEY-GRAPHS, BRAID GROUP, RING, EXTENSIONS, GENERATORS
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

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.