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 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume:
  • Publication Date: 2013
  • Doi Number: 10.1186/1029-242x-2013-118
  • Journal Name: JOURNAL OF INEQUALITIES AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: graphs, semi-direct product, monoid presentation, ZERO-DIVISOR GRAPH, CAYLEY-GRAPHS, SEMIGROUPS, RING
  • Bursa Uludag University Affiliated: Yes

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.