On the nonnegative signed domination numbers in graphs

• Main Authors: Maryam Atapour, Seyyed Mahmoud Sheikholeslami
• Format: Article
• Language: English
• Published: Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia 2016-10-01
• Series: Electronic Journal of Graph Theory and Applications
• Subjects: nonnegative signed dominating function, nonnegative signed domination number
• Online Access: https://www.ejgta.org/index.php/ejgta/article/view/112

<p>A nonnegative signed dominating function (NNSDF) of a graph $G$<br />is a function $f$ from the vertex set $V(G)$ to the set $\{-1,1\}$<br />such that $\sum_{u\in N[v]}f(u)\ge 0$ for every vertex $v\in<br />V(G)$. The nonnegative signed domination number of $G$, denoted by<br />$\gamma_{s}^{NN}(G)$, is the minimum weight of a nonnegative<br />signed dominating function on $G$. In this paper, we establish<br />some sharp lower bounds on the nonnegative signed domination<br />number of graphs in terms of their order, size and maximum and<br />minimum degree.</p>