Pelabelan Product Cordial Graf Gabungan Pada Beberapa Graf Sikel Dan Shadow Graph Sikel

Abtrak Misalkan graf G=V, E , Pelabelan product cordial adalah pelabelan titik biner f:EG→0, 1 yang menginduksi pelabelan sisi f*:EG→0, 1 dengan f*u,v=fu.fv, ∀u, v∈E(G) sehingga memenuhi syarat vf0-vf1≤1 dan ef0-ef1≤1 , dengan vf0,vf1,ef0,ef1 berturut – turut menyatakan banyaknya titik yang berlabel 0, banyaknya titik yang berlabel 1, banyaknya sisi yang berlabel 0 dan banyaknya sisi yang berlabel 1. Path gabungan dari graf G adalah graf yang diperoleh dengan menambahkan sisi antara Gi dan Gi+1 untuk i=1, 2, …, n-1 , dimana G1, G2, …, Gn, n≥2 dengan n salinan graf G. Shadow graph dari graf sikel dinotasikan dengan D2(Cn) adalah graf yang diperoleh dari dua graf sikel Cn\u27 dan Cn" dengan menghubungkan setiap titik uij\u27∈Cn\u27 dengan sebuah sisi ke titik yang adjacent dengan uij"∈Cn" (titik uij"∈Cn" adalah bayangan atau shadow dari uij\u27∈Cn\u27 ). Dalam Tugas Akhir ini dibahas tentang pelabelan product cordial pada beberapa graf sikel serta shadow graph sikel. Kata Kunci : pelabelan, cordial, sikel, biner, path, shadow graph. 1. PENDAHULUAN Pelabelan graf merupakan suatu topik dalam teori graf. Objek kajiannya berupa graf yang secara umum direpresentasikan oleh titik dan sisi serta himpunan bagian bilangan asli yang disebut label. Pertama kali diperkenalkan oleh Sadlack (1964), kemudian Stewart (1966), Kotzig dan Rosa (1970). Hingga saat ini pemanfaatan teori pelabelan graf sangat dirasakan peranannya, terutama pada sektor sistem komunikasi dan transportasi, navigasi geografis, radar, penyimpanan data komputer, dan desain integrated circuit pada komponen elektronik. Graf merupakan pasangan himpunan titik dan himpunan sisi. Pengaitan titik-titik pada graf membentuk sisi dan dapat direpresentasikan pada gambar sehingga membentuk pola graf tertentu. Pola-pola yang terbentuk didefinisikan dan dikelompokkan menjadi kelas-kelas graf. Beberapa kelas graf menurut banyaknya sisi yang insiden terhadap titik antara lain graf reguler, yang derajat setiap titiknya adalah sama dan graf irreguler, yang derajat setiap titiknya ada yang tidak sama. Terdapat pula graf petersen yang diperumum yang merupakan salah satu subkelas graf reguler. Pelabelan merupakan pemetaan injektif yang memetakan unsur himpunan titik dan atau unsur himpunan sisi ke bilangan asli. Pelabelan titik adalah pelabelan dengan domain himpunan titik, pelabelan sisi adalah pelabelan dengan domain himpunan sisi, dan pelabelan total adalah pelabelan dengan doamin gabungan himpunan titik dan himpunan sis

Konstruksi, Sifat Dan Dimensi Himpunan Cantor Middle Third

This paper discussed about the construction of Cantor middle third set which is formed from unit interval . To construct the Cantor set, take a line and remove the middle third and remain two line segments. This Process is repeated infinite number of times. This process produces some interesting properties on Cantor middle third set, such as has uncountable many elements, contains no intervals, and is compact, perfect, and nowhere dense. By using Hausdorff dimension and self similar set, it discussed the dimension of Cantor middle third set which is a unique positive numbe

Pelabelan Graceful Genap Baru Pada Graf Cmpn

Pelabelan Graceful pada graf dengan q sisi merupakan pemetaan injektif , yang mengakibatkan pemetaan , yang didefinisikan dengan bersifat bijektif. Graf yang memenuhi pelabelan graceful disebut graf graceful. T. Mahalaksmi Senthil Kumar, T. Abarna Parthiban dan T. Vanadhi [4], membuktikan graf CmÈPn merupakan graf graceful genap untuk m ganjil yang memenuhi kondisi tertentu. Marry U dan Saranya D [2], membuktikan bahwa graf CmÈPn merupakan graf graceful genap untuk m genap yang memenuhi kondisi tertentu. Pelabelan graceful genap didefinisikan sebagai pemetaan injektif yang mengakibatkan pemetaan , yang didefinisikan bersifat bijektif. Tetapi pada pembuktian [4] dan [2], syarat injektif dan bijektif fungsinya tidak terpenuhi. Artikel ini mendefinisikan kembali pelabelan graceful genap pada graf CmÈPn sehingga syarat injektif dan bijektif fungsinya terpenuhi

Analisa Kestabilan Model Matematika Untuk Penyembuhan Kanker Menggunakan Oncolytic Virotherapy

Oncolytic virotherapy is one type of cancer treatment using oncolytic virus. In this paper, we will present a mathematical model for treatment of cancer using oncolytic virotherapy with the burst size of a virus (the number of new viruses released from lysis of an infected cell) and we considering the presence of syncytia which is a fusion between infected tumor cell and uninfected tumor cell. In this mathematical model we introduced the population of uninfected tumor cells which fusion in syncytia. So, in this model contains four population, which are, uninfected tumor cell population, infected tumor cell population, uninfected tumor cell population which fusion in syncytia, and free virus particles which are outside cells. Then, these models are analyzed to determine the stability of the equilibrium points. The stability of the equilibrium points criteria is based on basic reproduction number () and we show that there exist a disease free equilibrium point and a disease endemic equilibrium point. By the Routh-Hurwitz criterion of stability, we prove that the disease free equilibrium point is locally asymptotically stable if and the disease endemic equilibrium point is locally asymptotically stable if . In this numerical simulations using software Maple we have, if then the graphic of this mathematical model will reach the disease free equilibrium point, then virotherapy fails. While, if then the graphic of this mathematical model will reach the disease endemic equilibrium point, then virotherapy success

Pelabelan Prime Cordial Pada Beberapa Graf Yang Terkait Dengan Graf Sikel

Prime cordial labeling of a graph is a bijective mapping of the set vertex to the set where is the number of vertex . The edge labeling induced the vertex labeling, which is obtained by finding the great common divisor (gcd) of the label of vertex which it\u27s adjacent. If gcd of the adjacent vertex label is 1 then the label of edge is 1, but if gcd of the adjacent vertex label value other than 1 then the label of edge is 0, and the absolute value of the difference between the number of edges labeled 0 and the number of edges labeled 1 is less than equal with 1. A graph admits prime cordial labeling is called prime cordial graph. In this paper, we study about edge duplication cycle graph (except for ), vertex duplication cycle graph , path union union of cycle the graph and friendship graph one point union of copies of cycle

Model Pertumbuhan Logistik Dengan Kontrol Optimal Penyebaran Demam Berdarah Dengue

Controlling of spread of dengue fever was sought by the government together with the people by, among others, campaigning “3M controlling” and eradicating of the vector population using insecticide and threating the infected people. The aim of this research is constructing the optimal control dynamic model by applying several strategies to control the spread of dengue fever. In this paper, the optimal control is constructed by using host logistic growth population model approach and then it is solved by using maximum Pontryagin principle. The results show that in the equilibrium condition, the effect of the control variable u1 (“3M campaigning” and eradicating of the mosquito by using insecticide) is strongly affected by the rate of the direct contact between host population and the infected and susceptible vector whereas the control variable u2 is strongly affected by the number of the infected host populatio

Analisis Kestabilan Model Dinamik Aliran Fluida Dua Fase Pada Sumur Panas Bumi

In this paper is discussed about the analysis of the stability of fluid flow dynamical model of two phases on the geothermal wells. The form of the model is non-linear differential equation. To analyze the local stability around the equilibrium point, first, the non linear models of is linearized around the equilibrium point using Taylor series. Further, from linearized model, we find a Jacobian matrix, where all of the real eigen values of the Jacobian matrix are zeros. So that the behviour of the dynamical system obtained around the equilibrium point is stable

Analisa Kinerja Sistem Kontrol Diskrit Chaos Lup Terbuka Dan Tertutup Dengan Pengendali Impulsif

Tability the discrete chaotic systems is interesting to be discussed, given that chaos is closely related to random and irregular state. Stability of discrete chaotic system can be obtained using impulsive control law and applying Lyapunov stability theory. So it can show sufficient conditions for the design of impulsive controllers and globally exponentially set-stable can be reached. Based on the results of the impulsive control, it is seen that the behavior of chaos in a discrete chaos system which originally the trajectory are irregular, can be control and become stable, and there is a globally exponentially attracting set earned in the system. The numerical simulation on the discrete chaotic system is presented to illustrate the effectiveness of the obtained results from control impulsive