Zero divisor graph associated to Γ−semigroup of Zn
Abstract
In this paper we have studied the zero divisor graph G1(Zn(Γ)) associated with a Γ−semigroup. Here we have taken two non empty sets Zn and set Γ of non zero zero divisors of Zn then Zn(Γ) is a Γ−semi group. In this paper we have taken all the elements of Zn as the vertices of the graph G1(Zn(Γ)) and two distinct vertices a and b are adjacent if and only if for any α∈Γ we have aαb=0. In this paper we have studied the degree of vertices of G1(Zn(Γ)), number of edges, girth, diameter, planarity, and traversibility of G1(Zn(Γ)).
Copyright © 2021 Pinku Chandra Dey, Kuntala Patra. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
P. C. Dey, K. Patra, Zero divisor graph associated to Γ−semigroup of Zn, J. Math. Comput. Sci. 11 (2021), 3767–3774. https://doi.org/10.28919/jmcs/5746
BibTeX
@article{Dey2021,
author = {Dey, Pinku Chandra and Patra, Kuntala},
title = {Zero divisor graph associated to Γ−semigroup of Zn},
journal = {J. Math. Comput. Sci.},
volume = {11},
year = {2021},
pages = {3767--3774},
doi = {10.28919/jmcs/5746}
}