A total dominating set of a graph G with no isolated vertices is subset S the vertex such that every adjacent to in S. The domination number minimum cardinality set. In this paper, we study middle graphs. Indeed, obtain tight bounds for terms order graph. We also compute some known families graphs explicitly. Moreover, Nordhaus-Gaddum-like relations are presented

Let $G = (V, E)$ be a simple graph of order $n$. The total dominating set is a subset $D$ of $V$ that every vertex of $V$ is adjacent to some vertices of $D$. The total domination number of $G$ is equal to minimum cardinality of total dominating set in $G$ and denoted by $gamma_t(G)$. The total domination polynomial of $G$ is the polynomial $D_t(G,x)=sum d_t(G,i)$, where $d_t(G,i)$ is the numbe...

background: satureja bachtiarica bunge, an endemic species with relatively wide distribution, is traditionally used as a medicinal and spice plant in iran. objective: essential oils composition, antioxidant activities and phenolics content of wild and cultivated s. bachtiarica of yazd origin were determined in this study. methods: hydrodistilled essential oils were analyzed by gc-fid and gc-ms....

this study examined if pre-germination altered the water content and water activity, contents of phytate, total phenolic, (±)-catechin, quercetin and total antioxidant capacity of almond  (prunus dulcis)kernel. raw almond kernels were submerged for 15 hours in water, 0.02 mol dm-3 phosphate buffer solution (ph 5.0) and 0.02 mol dm-3 phosphate buffer solution (ph 7.0) at 25 and 40ºc, respectivel...

abstract beneficial effects of humic substances on plant growth have been recognized by many researchers. a greenhouse experiment was conducted with humic acid (0, 20 and 50 mg/l) on lettuce cultivars ‘lollorossa’ and ‘javelina’ using completely randomized design at university of guilan. results showed that humic acid affected (p<5%) leaf number, height and nutrient uptake as well as ca, p and ...

let $k$ be a positive integer. a subset $s$ of $v(g)$ in a graph $g$ is a $k$-tuple total dominating set of $g$ if every vertex of $g$ has at least $k$ neighbors in $s$. the $k$-tuple total domination number $gamma _{times k,t}(g)$ of $g$ is the minimum cardinality of a $k$-tuple total dominating set of $g$. if$v(g)=v^{0}={v_{1}^{0},v_{2}^{0},ldots ,v_{n}^{0}}$ and $e(g)=e_{0}$, then for any in...