Browsing by Author "Atapour, Maryam"

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Access status: Open Access ,
Bounds on the inverse signed total domination numbers in graphs
(2016) Atapour, Maryam; Norouzian, Sepideh; Sheikholeslami, Seyed Mahmoud; Volkmann, Lutz
Let $G=(V,E)$ be a simple graph. A function $f:V\rightarrow \{-1,1\}$ is called an inverse signed total dominating function if the sum of its function values over any open neighborhood is at most zero. The inverse signed total domination number of $G$, denoted by $\gamma_{st}^0(G)$, equals to the maximum weight of an inverse signed total dominating function of $G$. In this paper, we establish upper bounds on the inverse signed total domination number of graphs in terms of their order, size and maximum and minimum degrees.
Access status: Open Access ,
Trees whose 2-domination subdivision number is 2
(2012) Atapour, Maryam; Sheikholeslami, Seyed Mahmoud; Khodkar, Abdollah
A set S of vertices in a graph $G=(V,E)$ is a $2$-dominating set if every vertex of $V\setminus S$ is adjacent to at least two vertices of $S$. The $2$-domination number of a graph $G$, denoted by $\gamma_2(G)$, is the minimum size of a $2$-dominating set of $G$. The $2$-domination subdivision number $sd_{\gamma_2}(G)$ is the minimum number of edges that must be subdivided (each edge in $G$ can be subdivided at most once) in order to increase the $2$-domination number. The authors have recently proved that for any tree $T$ of order at least $3$, $1 \leq sd_{\gamma_2}(T)\leq 2$. In this paper we provide a constructive characterization of the trees whose $2$-domination subdivision number is $2$.