On the nonnegative signed domination numbers in graphs

Maryam Atapour (Department of Mathematics, Faculty of Basic Sciences, University of Bonab, Bonab, Iran)
Seyyed Mahmoud Sheikholeslami (Department of Mathematics Azarbaijan Shahid Madani University Tabriz, I.R. Iran)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 4, No 2 (2016): Electronic Journal of Graph Theory and Applications

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