A Roman dominating function (RDF) on a graph $G = (V, E)$ is a labeling $f : V rightarrow {0, 1, 2}$ suchthat every vertex with label $0$ has a neighbor with label $2$. The weight of $f$ is the value $f(V) = Sigma_{vin V} f(v)$The Roman domination number, $gamma_R(G)$, of $G$ is theminimum weight of an RDF on $G$.An RDF of minimum weight is called a $gamma_R$-function.A graph G is said to be $g...

The purpose of this report is to present the results of analysis of actual glucosamine and/or chondroitin contents of several such products in the market place and to determine if they significantly deviate from their label claim. A total of fourteen products containing glucosamine sulfate and nine products containing chondroitin sulfate were evaluated. The amounts of glucosamine and chondroiti...

The purpose of this report is to present the results of analysis of actual glucosamine and/or chondroitin contents of several such products in the market place and to determine if they significantly deviate from their label claim. A total of fourteen products containing glucosamine sulfate and nine products containing chondroitin sulfate were evaluated. The amounts of glucosamine and chondroiti...