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 � (PM). 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. MSC: 05C10; 05C12; 05C25; 20E22; 20M05
Highlights
1 Introduction and preliminaries In this paper, we mainly investigate the interplay between the semi-direct product over monoids and the graph-theoretic properties of the semi-direct product in terms of its relations
One can define a new graph associated with this semi-direct product
By the graphtheoretic properties, we will be interested in the diameter, maximum and minimum degrees, girth, chromatic number, clique number, domination number, degree sequence and irregularity index of the corresponding new graph
Summary
Introduction and preliminariesIn this paper, we mainly investigate the interplay between the semi-direct product over monoids and the graph-theoretic properties of the semi-direct product in terms of its relations. The graph constructed in here is different from those in the previous studies and is interesting in terms of using algebraic semi-direct products during the construction of the vertex and edge sets. Let us recall the semi-direct product of any two monoids and its presentation.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
