Judul: The Effect of Applications Methylobacterium spp to Improvement of Soybean Vigour and Production
Abstrak: Methylobacterium spp is one of bacteria that produces phytohormon which have potency to stimulate seed germination and plant growth. The objective of this research was to study the effectiveness of Methylobacterium spp isolates in improving vigour and seed production of soybean. The Research conducted since September 2010 until April 2011. The research consisted of two experiments : (1) The effect of application Methylobacterium spp bacteria isolates to soybean seed germination. The research materials are six soybean varieties i.e : Sinabung, Kaba, Tanggamus, Anjasmoro, Grobogan dan Burangrang and four isolates Methylobacterium spp i.e: TD-J2, TD-K2, TD-TPB3, NTB-K1 and control (aquades); (2) The effect of application techniques Methylobacterium spp to soybean production. The research consisted of six level : 1) without seed soaking isolate + foliar spraying at 10 DAS + 20 DAS, 2) seed soaking isolate + foliar spraying at 10 DAS + 20 DAS; 3) seed soaking isolate; 4) splashing isolate to soil at 10 DAS + 20 DAS; 5) sterile soil isolate + splashing isolate to soil at 10 DAS + 20 DAS; and 6) control (water splashing). The results showed that Methylobacterium spp soaking in TD-K2 isolate on Kaba increased vigour index 17.33% (from 72% to 89.33%) and TD-J2 isolate increased speed of germination 9.49%/etmal (from 31.74 % etmal to 41.23 %/etmal). Application techniques of Methylobacterium spp with TD-TPB3 isolate on Kaba using seed soaking isolate + foliar spraying at 10 DAS + 20 DAS increased growth and production of soybean.
Keyword: 

Judul: he Effectiveness of Methylobacterium spp Isolate to Increase Production of Soybean (Glycine max L.).
Abstrak: Methylobacterium spp is one of bacteria that produces phytohormon which have potency to stimulate seed germination and plant growth to increase plant production. The aim of the research was to evaluate effectiveness of Methylobacterium spp and rates of fertilizer to increase soybean yield in field production. The research consisted of two experiments : (1) The effect of Methylobacterium spp application technique and rates of fertilizers on the soybean growth and production, (2) Effectiveness of Methylobacterium spp application technique to soybean yield in field production. The experiments were conducted in July 2012 to March 2013. The first experiment used Split Plot Design. The main plot was Methylobacterium spp application technique consisted of without Methylobacterium spp, seed soaking and spraying Methylobacterium spp at 15 and 30 days after planting (DAP), seed soaking and spraying Methylobacterium spp at 15 DAP and soaking seeds with Methylobacterium spp. The subplot was the rates of fertilizer N, P and K consisted of 0, 25, 50, 75 and 100% recommended rate of fertilizer (Rate of recommendation : 50 kg N ha-1, 100 kg P2O5 ha-1 dan 100 kg K2O ha-1). The second experiment used randomize complete block design. The experiment used two cultivation technologies are Methylobacterium spp and farmers. Methylobacterium spp cultivation technology used the best result of the experiment 1, seed soaking and spraying Methylobacterium spp at 15 DAP and 75% recommended rate of fertilizer. The farmers technology used 100% recommended rate of fertilizer. The results showed that seed soaking and spraying Methylobacterium spp at 15 DAP and 15+30 DAP significantly increased the age and total of flowering, total of pod , total of seed and weight of seed than without isolate application. The rate of fertilizer 50, 75 and 100% gives the same response at height of plant 56 DAP, total branches per plant and weight of seed per plant but significantly increase than without application. The seed soaking and spraying Methylobacterium spp technology and rate of fertilizer 75% significantly increased total production and seed vigour of soybean compared with the farmers technology.
Keyword: bacteria, cultivation technology, rates of fertilizer N, P and K

Judul: Cycle Hamilton pada Graf Lengkap, Graf Regular, dan Graf 2-Connected 4-Regular Berorder Kurang dari Sepuluh
Abstrak: Suatu graf disebut graf Hamilton apabila graf tersebut memuat cycle Hamilton, yaitu cycle yang melewati setiap vertex tepat satu kali. Menentukan keberadaan cycle Hamilton pada suatu graf dapat menggunakan syarat cukup yang berupa teorema-teorema yang telah diperkenalkan sejak tahun 1950-an. Beberapa syarat cukup yang dibahas dalam karya ilmiah ini adalah syarat cukup yang berhubungan dengan graf lengkap dan graf regular. Suatu graf lengkap berorder 𝑛������ ≥ 3 dan graf r-regular berorder 𝑛������ ≤ 2𝑟������ + 1 merupakan graf Hamilton, Karena kedua graf tersebut memuat cycle Hamilton. Selanjutnya, syarat cukup tersebut digunakan untuk menentukan keberadaan cycle Hamilton pada graf 2-connected 4- regular berorder kurang dari 10.
Keyword: graf Hamilton, graf regular, graf lengkap, graf 2-connected 4-regular