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Jurnal Matematika
Published by Universitas Diponegoro
ISSN : -     EISSN : -     DOI : -
Core Subject : Education,
Mathematics
Arjuna Subject : -
Articles 4 Documents
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Search results for , issue "Vol 4, No 2 (2015): JURNAL MATEMATIKA" : 4 Documents clear
SIFAT DAN PEWARNAAN TOTAL PADA GRAF TITIK GANDA Dewi Kusuma Handayani
Jurnal Matematika Vol 4, No 2 (2015): JURNAL MATEMATIKA
Publisher : MATEMATIKA FSM, UNDIP

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Abstract

 ABSTRACT. Graf titik ganda yang dinotasikan dengan  adalah graf yang diperoleh dari  yang himpunan titiknya terdiri dari semua himpunan bagian dari . Titik dalam graf titik ganda dinotasikan dengan , dimana , sehingga dua titik yang berbeda di graf titik ganda dan  dikatakan adjacent jika dan hanya jika , dan jika , maka  dan adjacent di . Pewarnaan total pada graf  adalah pemetaan dari  ke himpunan  sedemikian sehingga tidak ada dua titik atau dua sisi yang adjacent menerima warna yang sama, dan pemberian warna pada suatu titik dan sisi yang incident diberikan warna yang berbeda.. Tugas akhir ini membahas sifat pada graf titik ganda dan pewarnaan total pada graf titik ganda dari graf path, graf sikel, dan graf bintang. kemudian setelah dilakukan analisis dapat ditemukan bilangan kromatik total pada  , , dan  adalah derajat maksimal . Dalam kehidupan nyata, pewarnaan total dapat diterapkan pada penjadwalan.Keywords: graf titik ganda, pewarnaan total, bilangan kromatik total
MODEL DINAMIK PADA SISTEM PROSES PENGOLAHAN AIR LIMBAH KOLAM STABILISASI FAKULTATIF Dian Huliyun Rahmania
Jurnal Matematika Vol 4, No 2 (2015): JURNAL MATEMATIKA
Publisher : MATEMATIKA FSM, UNDIP

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MODEL DINAMIK PADA SISTEM PROSES PENGOLAHAN AIR LIMBAH KOLAM STABILISASI FAKULTATIF                                                           Dian Huliyun Rahmania1, Sunarsih2, Nikken Prima Puspita31,2,3Program Studi Matematika FSM Universitas DiponegoroJl. Prof. H. Soedarto, S.H. Tembalang Semarang dianhuliyun@gmail.comsunarsihmat@gmail.com ABSTRACT. Domestic wastewater is wastewater generated from a household activities that can pollute the environment. If this wastewater pollution did not dealt seriously can cause several problems. To overcome these problems, the wastewater needs to undergo treatment processing in advance. One of the treatment processing system is using units Wastewater Treatment Plant (WWTP). The purpose of this thesis is to contruct dynamic model of wastewater treatment on facultative stabilization ponds in simulating these model and then validate it. The result of model simulation shows that there is an error rate of <10% by comparing model and observation data toward algae, bacteria, dissolved oxygen, and substrate. Model is done numerically using euler method. Keywords: Domestic Wastewater, Facultative Stabilization Ponds, Dynamic Modeling, Euler Method. 
ANALISA KESTABILAN MODEL MATEMATIKA PENYAKIT PNEUMONIA DENGAN CARRIERS Hanik Rahmawati
Jurnal Matematika Vol 4, No 2 (2015): JURNAL MATEMATIKA
Publisher : MATEMATIKA FSM, UNDIP

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Abstract

 ABSTRACT. Pneumonia disease is lung infammation disease caused by microorganism such as Streptococcus pneumoniae bactery. This final project presented a mathematical model that describe dinamic pneumonia disease population in children under five years. The model used SICR are susceptible, infected, carriers, and recovered. Analysis to the model is conducted to decide whether pneumonia will spread within population with reproduction number. Using Routh-Hurwitz criterion we obtained free disease equilibrium and endemic equilibrium. From stability analysis of simulation result it is known that the disease free eqilibrium unstable while the endemic equilibrium stable local asimtotic with . 
BILANGAN DOMINASI DAN BILANGAN DOMINASI HIPER SEMIGRAF BIPARTIT Indah Permatasari1
Jurnal Matematika Vol 4, No 2 (2015): JURNAL MATEMATIKA
Publisher : MATEMATIKA FSM, UNDIP

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Abstract

BILANGAN DOMINASI DAN BILANGAN DOMINASI HIPER SEMIGRAF BIPARTIT Indah Permatasari1, Djuwandi2, Robertus Heri S.U3 Jurusan Matematika FSM Universitas DiponegoroJl. Prof. H. Soedarto, S.H. Tembalang Semarang permatassariindah@gmail.comrobertusutomo@yahoo.co.id ABSTRACT. Semigraph  is a pair  where  is a nonempty set whose elements are called vertices of  and  is a set of ordered n-tuples called edges of . A Semigraph  called bipartite semigraph if its vertex set  can be partitioned into set  such that  and  are independent sets. A set  is a dominating set of  if  adjacent with . If there is not exist  is a dominating set such that  is a minimal dominating set of  and minimum cardinality of a minimal dominating set is called the domination number of   and it is denoted by . A set  is a hyper dominating set of  if  hyper dominated by . If there is not exist  is hyper dominating set such that  is a minimal hyper dominating set of  and minimum cardinality of a minimal hyper dominating set is called the hyper domination number of   and it is denoted by . The study in this thesis that  and  are less than or equal to half of the number of vertices in vertex set . Furthermore, studied application of domination number and hyper domination number for products of selling network in the insurance business.Keywords: semigraph, bipartite semigraph, dominating set, domination number, hyper dominating set, hyper domination number

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