On the nonnegative signed domination numbers in graphs

Main Authors: Atapour, Maryam; Department of Mathematics, Faculty of Basic Sciences, University of Bonab, Bonab, Iran, Sheikholeslami, Seyyed Mahmoud; Department of Mathematics Azarbaijan Shahid Madani University Tabriz, I.R. Iran
Format: Article info application/pdf eJournal
Bahasa: eng
Terbitan: GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB , 2016
Subjects:
Online Access: http://www.ejgta.org/index.php/ejgta/article/view/112
http://www.ejgta.org/index.php/ejgta/article/view/112/pdf_27
Daftar Isi:
  • 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.