A new graph based on the semi-direct product of some monoids


GÜZEL KARPUZ E., Das K. C. , CANGÜL İ. N. , ÇEVİK A. S.

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2013 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume:
  • Publication Date: 2013
  • Doi Number: 10.1186/1029-242x-2013-118
  • Title of Journal : JOURNAL OF INEQUALITIES AND APPLICATIONS
  • Keywords: graphs, semi-direct product, monoid presentation, ZERO-DIVISOR GRAPH, CAYLEY-GRAPHS, SEMIGROUPS, RING

Abstract

In this paper, firstly, we define a new graph based on the semi-direct product of a free abelian monoid of rank n by a finite cyclic monoid, and then discuss some graph properties on this new graph, namely diameter, maximum and minimum degrees, girth, degree sequence and irregularity index, domination number, chromatic number, clique number of Gamma (P-M). Since graph theoretical studies (including such above graph parameters) consist of some fixed point techniques, they have been applied in fields such as chemistry (in the meaning of atoms, molecules, energy etc.) and engineering (in the meaning of signal processing etc.), game theory and physics.