Maryam Atapour
Department of Mathematics, Faculty of Basic Sciences, University of Bonab, Bonab, Iran

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On the nonnegative signed domination numbers in graphs Maryam Atapour; Seyyed Mahmoud Sheikholeslami
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 4, No 2 (2016): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2016.4.2.10

Abstract

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.