‎a set $s$ of vertices of a graph $g=(v,e)$ without isolated vertex‎ ‎is a {em total dominating set} if every vertex of $v(g)$ is‎ ‎adjacent to some vertex in $s$‎. ‎the {em total domatic number} of‎ ‎a graph $g$ is the maximum number of total dominating sets into‎ ‎which the vertex set of $g$ can be partitioned‎. ‎we show that the‎ ‎total domatic number of a random $r$-regular graph is almost‎...

Root traits influence the amount of water and nutrient absorption, and are important for maintaining crop yield under drought conditions. The objectives of this research were to characterize variability of root traits among spring wheat genotypes and determine whether root traits are related to shoot traits (plant height, tiller number per plant, shoot dry weight, and coleoptile length), region...

in order to study of variation and relationships between morphological traits with yield and its components in three grain sorghum cultivars (kimia, sepideh and payam) and nine promising lines (mgs1-mgs9) received from seed and plant improvement institute, an experiment was conducted as randomized complete block design with four replications in birjand agricultural research station, in two grow...

A {em Roman dominating function} on a graph $G$ is a function $f:V(G)rightarrow {0,1,2}$ satisfying the condition that every vertex $u$ for which $f(u)=0$ is adjacent to at least one vertex $v$ for which $f(v)=2$. A {em total Roman dominating function} is a Roman dominating function with the additional property that the subgraph of $G$ induced by the set of all vertices of positive weight has n...

Wheat (Triticum aestivum L. emend. Thell.) grain yields are highly dependent upon the number of spike-bearing tillers produced per plant. Salinity, drought, and other environmental stresses can greatly affect the development and viability of tillers. We determined the effects of soil salinity on the occurrence and rate of tiller development and the incidence of tiller abortion in spring wheat c...

Tiller number is one of the key factors that influences rice plant type and yield components. In this study, an EMS-induced rice tiller suppression mutant ts1 was characterized. Morphological and histological observations revealed that, in the ts1 plants, the tiller buds were abnormally formed and therefore cannot outgrow into tillers. With an F2 population derived from a cross between ts1 and ...