ON THE STRONG DOMINATING SETS OF GRAPHS

Author(s):

Hassan Zaherifar , Saeid Alikhani * , Nima Ghanbari

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:
Let $G=(V(G),E(G))$ be a simple graph. A set $D\subseteq V(G)$ is a strong dominating set of $G$, if for every vertex $x\in V(G)\setminus D$ there is a vertex $y\in D$ with $xy\in E(G)$ and $deg(x)\leq deg(y)$. The strong domination number $\gamma_{st}(G)$ is defined as the minimum cardinality of a strong dominating set. In this paper, we calculate $\gamma_{st}(G)$ for specific graphs and study the number of strong dominating sets of some graphs.
Keywords:

Dominating set , strong domination number , product

Language:
English
Published:
Journal of Algebraic Systems, Volume:11 Issue: 1, Summer-Autumn 2023
Pages:
65 to 76
https://www.magiran.com/p2540611  
سامانه نویسندگان
  • Saeid Alikhani
    Corresponding Author (2)
    Professor Department of Mathematics, Yazd University, University of Yazd, Yazd, Iran
    Alikhani، Saeid
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