M Chellali
LAMDA-RO Laboratory, Department of Mathematics, University of Blida, B.P. 270, Blida, Algeria
[ 1 ] - k-Efficient partitions of graphs
A set $S = \{u_1,u_2, \ldots, u_t\}$ of vertices of $G$ is an efficient dominating set if every vertex of $G$ is dominated exactly once by the vertices of $S$. Letting $U_i$ denote the set of vertices dominated by $u_i$, we note that $\{U_1, U_2, \ldots U_t\}$ is a partition of the vertex set of $G$ and that each $U_i$ contains the vertex $u_i$ and all the vertices at distance~1 from it in $G$. I…
[ 2 ] - Outer independent Roman domination number of trees
A Roman dominating function (RDF) on a graph $G=(V,E)$ is a function $f:V\rightarrow \{0,1,2\}$ such that every vertex $u$ for which $f(u)=0$ is adjacent to at least one vertex $v$ for which $f(v)=2$. An RDF $f$ is called an outer independent Roman dominating function (OIRDF) if the set of vertices assigned a $0$ under $f$ is an independent set. The weight of an OIRDF is the sum of its function v…
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