The graph based on Gröbner-Shirshov bases of groups Proceedings of the International Congress in Honour of Professor Hari M. Srivastava

Abstract

Let us consider groups [InlineEquation not available: see fulltext.], [InlineEquation not available: see fulltext.], [InlineEquation not available: see fulltext.], [InlineEquation not available: see fulltext.] and [InlineEquation not available: see fulltext.], where [InlineEquation not available: see fulltext.]. In this paper, by defining a new graph [InlineEquation not available: see fulltext.] based on the Gröbner-Shirshov bases over groups [InlineEquation not available: see fulltext.], where [InlineEquation not available: see fulltext.], we calculate the diameter, maximum and minimum degrees, girth, chromatic number, clique number, domination number, degree sequence and irregularity index of [InlineEquation not available: see fulltext.]. 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. MSC: 05C25, 13P10, 20M05, 20E06, 26C10. © 2013 G Karpuz et al.; licensee Springer.