No abstract

Let T_m=(V(T_m), E(T_m)) be a triangular grid graph of m ϵ N level. The order of graph T_m is called a triangular number. A subset T of V(T_m) is a dominating set of T_m  if for all u_V(T_m)\T, there exists vϵT such that uv ϵ E(T_m), that is, N[T]=V(T_m).  A dominating set T of V(T_m) is a secure dominating set of T_m if for each u ϵ V(T_m)\T, there exists v ϵ T such that uv ϵ E(T_m) and the set (T\{u})ꓴ{v} is a dominating set of T_m. The minimum cardinality of a secure dominating set of T_m, denoted by γ_s(T_m)  is called a secure domination number of graph T_m. A secure dominating number  γ_s(T_m) of graph T_m is a triangular secure domination number if γ_s(T_m) is a triangular number. In this paper, a combinatorial formula for triangular secure domination number of graph T_m was constructed. Furthermore, the said number was evaluated in relation to perfect numbers.

Low crop productivity in most marginal uplands is primarily due to poor agro-ecological conditions. There is a need to improve farming practices of upland farmers to improve their quality of life thus, the study was conducted in the marginal uplands of Brgy. Linao, Inopacan, Leyte, Philippines from February to July 2013, to determine the best cropping system that would improve crop productivity and to promote the best cropping system technology to upland farmers. The experimental units were arranged in Randomized Complete Block Design with three replications. The treatments were intercropping (upland rice + mungbean, corn + mungbean) and monocropping (upland rice, corn and mungbean). The growth and yield parameters were not significantly influenced by the cropping systems. Thus, crop growth and development in either intercropping or monocropping schemes were comparable. However, corn + mungbean gave a land equivalent ratio (LER) of 1.53, which means that such cropping system is more productive than growing corn or mungbean as monocrop. On the other hand, growing upland rice alone was more productive than upland rice + mungbean as indicated by a LER of 0.93.Corn + mungbean gave a net income of PhP8,452.18 per hectare.