Given a graph $G=(V,E)$ and a vertex $v in V$, by $N(v)$ we represent the open neighbourhood of $v$. Let $f:Vrightarrow {0,1,2}$ be a function on $G$. The weight of $f$ is $omega(f)=sum_{vin V}f(v)$ and let $V_i={vin V colon f(v)=i}$, for $i=0,1,2$. The function $f$ is said to bebegin{itemize}item a Roman ${2}$-dominating function, if for every vertex $vin V_0$, $sum_{uin N(v)}f(u)geq 2$. The R...

A total acquisition move in a weighted graph G moves all weight from a vertex u to a neighboring vertex v, provided that before this move the weight on v is at least the weight on u. The total acquisition number, at(G), is the minimum number of vertices with positive weight that remain in G after a sequence of total acquisition moves, starting with a uniform weighting of the vertices of G. For ...

Background: &beta-glucans are glucose polymers with a variety of stimulatory effects on the immune system. The objective of this study was to evaluate the immune-enhancing activities of low molecular weight gamma irradiated &beta-glucan (I&beta-g) extracted from Pleurotus ostreatus in response to Pseudomonas aeruginosa infection in rats. Materials and Methods: &beta-glucan (&beta-g) powder was ...

On a weighted graph G, a total acquisition move transfers weight from a vertex u to a neighbor v provided that the weight on v is at least as much as the weight on u. Starting with all vertices having weight 1, the total acquisition number of G, denoted at(G), is the minimum number of vertices with positive weight after a sequence of total acquisition moves. In [D. Lampert and P. Slater, Congr....