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All Journal Journal of Degraded and Mining Lands Management JURNAL ILMIAH MATEMATIKA DAN TERAPAN
N Farida
Mataram Univ
Agriculture, Biological Sciences & Forestry Biochemistry, Genetics & Molecular Biology Mathematics

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PELABELAN SELIMUT AJAIB SUPER PADA GRAF LINTASAN Farida, N; Sudarsana, I W; Resnawati, Resnawati
JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 15 No. 2 (2018)
Publisher : Program Studi Matematika, Universitas Tadulako

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (655.298 KB) | DOI: 10.22487/2540766X.2018.v15.i2.11347

Abstract

Let 𝐺 = (𝑉, 𝐸) be a simple graph. An edge covering of 𝐺 is a family of subgraphs 𝐻1 , … , 𝐻𝑘 such that each edge of 𝐸(𝐺) belongs to at least one of the subgraphs 𝐻𝑖 , 1 ≤ 𝑖 ≤ 𝑘. If every 𝐻𝑖 is isomorphic to a given graph 𝐻, then the graph 𝐺 admits an 𝐻 − covering. Let 𝐺 be a containing a covering 𝐻, and 𝑓 the bijectif function 𝑓: (𝑉 ∪ 𝐸) → {1,2,3, … , |𝑉| + |𝐸|} is said an 𝐻 −magic labeling of 𝐺 if for every subgraph 𝐻 ′ = (𝑉 ′ ,𝐸 ′ ) of 𝐺 isomorphic to 𝐻, is obtained that ∑ 𝑓(𝑉) + ∑ 𝑓(𝐸) 𝑒∈𝐸(𝐻′ 𝑣∈𝑉(𝐻 ) ′ ) is constant. 𝐺 is said to be 𝐻 −super magic if 𝑓(𝑉) = {1, 2, 3, … , |𝑉|}. In this case, the graph 𝐺 which can be labeled with 𝐻-magic is called the covering graph 𝐻 −magic. The sum of all vertex labels and all edge labels on the covering 𝐻 − super magic then obtained constant magic is denoted by ∑ 𝑓(𝐻). The duplication graph 2 of graph 𝐷2 (𝐺) is a graph obtained from two copies of graph 𝐺, called 𝐺 and 𝐺 ′ , with connecting each respectively vertex 𝑣 in 𝐺 with the vertexs immediate neighboring of 𝑣 ′ in 𝐺 ′ . The purpose of this study is to obtain a covering super magic labeling for of 𝐷2 (𝑃𝑚) on (𝐷2 (𝑃𝑛 )) for 𝑛 ≥ 4 and 3 ≤ 𝑚 ≤ 𝑛 − 1. In this paper, we have showed that duplication path graph (𝐷2 (𝑃𝑛 )) has 𝐷2 (𝑃𝑚) covering super magic labeling for 𝑛 ≥ 4 and 3 ≤ 𝑚 ≤ 𝑛 − 1 with constant magic for all covering is ∑ 𝑓(𝐷2 (𝑃𝑚) (𝑠) ) = ∑ 𝑓(𝐷2 (𝑃𝑚) (𝑠+1) )
Effectiveness of organic wastes and forages to increase soil fertility status and crop yield in dry lands Ernawati, N M L; Ngawit, I K; Farida, N
Journal of Degraded and Mining Lands Management Vol. 1 No. 4 (2014)
Publisher : Brawijaya University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15243/jdmlm.2014.014.165

Abstract

The main purpose of this study was to elucidate the effects of application of organic wastes and rotation of cropping system on soil fertility status and yields of dry field rice, maize, soybean, groundnut and mungbean in order to overcome soil degradation problems in dry land areas. Six cropping rotation systems (dry field rice-soybean-fallow, dry field rice-groundnut-fallow, dry field rice-mungbean-fallow, maize-soybean-fallow, maize-groundnut-fallow, and maize-mungbean-fallow), and six organic fertilizer rates (0, 5, 10, 15, 20 t/ha, and 25 t/ha) were arranged in a randomized block design with two replicates. The results showed that maize-groundnut-fallow and dry filed rice-groundnut-fallow cropping systems with application of 25 t/ha organic fertilizer were able to increase soil fertility status. At the two cropping systems, status of N-total, P-total, K-total, C-total, CEC, and soil pH were better than other treatments. Soil physical fertility status on maize-groundnut-fallow and dry filed rice-groundnut-fallow cropping systems with application of 25 t/ha organic fertilizer was better than other treatments. Implication of improvement of soil physic characteristic because of this treatment was capable of raising irrigation efficiency about 0.98. Soil biological fertility at the same treatments was also better than other treatments. The average of soil worms was 2.44 per m2 soil. The amount of bacteria was 3.284 x 106 per gram soil. The amount of colony was 545.78 and the average of colony forming holozone was 19.66. Application of 20-25 t/ha organic fertilizer yielded higher crop yields than application of 0, 5, 10, an 15 t/ha organic fertilizer. Maize-groundnut-fallow cropping system and 25 t/ha application of organic fertilizer resulted in the highest propriety index, with value BC-ratio 2.54, BEPproduction 61760, and BEPvalue 982.
Co-Authors I K Ngawit N M L Ernawati Resnawati Sudarsana, I W