Some results on secure domination in zero-divisor graphs
Abstract
Let Γ(G) = (V(Γ(G)),E(Γ(G))) be a zero-divisor graph. A dominating set S of V(Γ(G)) is a secure dominating set of Γ(G) if for every vertex x ∈V(Γ(G))−S, there exists y ∈ NΓ(G) (x)∩S such that (S−{y})∪{x} is a domination set. The minimum cardinality of a secure dominating set of Γ(G) is called secure domination number. In this paper, the secure domination number of zero-divisor graphs is obtained and also studied the structure of this parameter in Γ(Zn).
Copyright © 2021 A. Mohamed Ali, S. Rajkumar. 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
A. M. Ali, S. Rajkumar, Some results on secure domination in zero-divisor graphs, J. Math. Comput. Sci. 11 (2021), 4799–4809. https://doi.org/10.28919/jmcs/5904
BibTeX
@article{Ali2021,
author = {Ali, A. Mohamed and Rajkumar, S.},
title = {Some results on secure domination in zero-divisor graphs},
journal = {J. Math. Comput. Sci.},
volume = {11},
year = {2021},
pages = {4799--4809},
doi = {10.28919/jmcs/5904}
}