On the nonnegative signed domination numbers in graphs

Maryam Atapour, Seyyed Mahmoud Sheikholeslami


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 $v\in
V(G)$. The nonnegative signed domination number of $G$, denoted by
$\gamma_{s}^{NN}(G)$, is the minimum weight of a nonnegative
signed dominating function on $G$. In this paper, we establish
some sharp lower bounds on the nonnegative signed domination
number of graphs in terms of their order, size and maximum and
minimum degree.


nonnegative signed dominating function, nonnegative signed domination number

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DOI: http://dx.doi.org/10.5614/ejgta.2016.4.2.10


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