Representasi Matriks Graf Cut-Set Dan Sirkuit

Representasi matriks pada beberapa kelas graf, khususnya graf cut-set dan sirkuit pada dasarnya dilakukan dalam rangka untuk mengkaji salah satu bagian dari ilmu tentang graf, dimana graf sangat banyak kegunaannya dalam kehidupan sehari-hari. Representasi ini dilakukan dengan cara mengobservasi suatu graf cut-set dan sirkuit yang dipilih sesuai dengan kebutuhannya, dalam hal ini adalah jenis graf lengkap. Sehingga dengan beberapa contoh graf yang diobservasi, sudah dapat diteliti informasi yang diberikan oleh matriks yang dihasilkan. Observasi ini memperlihatkan bahwa, representasi graf cut-set dan sirkuit dalam bentuk matriks memiliki pola khusus. Kata Kunci : Graf, Cut-Set, Sirkui

BEBERAPA IDENTITAS BARISAN FIBONACCI DAN LUCAS

Penelitian ini bertujuan untuk menyelidiki hubungan antara barisan Fibonacci dan Lucas, dan membuktikan identitas-identitas barisan Fibonacci dan Lucas. Barisan Fibonacci dan Lucas merupakan barisan rekursif yang mempunyai aturan yang sama namun memiliki nilai awal yang berbeda. Dalam penelitian ini, akan dibahas beberapa identitas yang melibatkan kedua barisan tersebut, serta satu identitas yang berkaitan dengan segitiga Pascal

Counting the Number of Disconnected Labeled Graphs of Order Five without Paralel Edges

Abstract— Given a graph G(V,E) with n vertices and m edges, where every vertex is labeled, there are a lot of possible graphs that can be constructed, either connected graphs or disconnected, simple or not simple. A graph G(V,E) is called as a connected graph if there exists at least one path between every pair of vertices in G, and otherwise, G is disconnected. A graph G is called as a labeled graph if every node/vertex and or every edge is labeled. In this research, we are concerning about a graph where every vertex is labeled. Parallel edges are two edges or more which have the same end points. In this research we found that the number of disconnected labeled graph without parallel edges for  and  can be obtained with the following formula: {{.    is the number of disconnected labeled graph without parallel edges for  and . Keywords—  counting graph, labeled graph, disconnected, parallel edge

The Modified CW1 Algorithm for the Degree Restricted Minimum Spanning Tree Problem

Given edge weighted graph G (all weights are non-negative), The Degree Constrained Minimum Spanning Tree Problem is concerned with finding the minimum weight spanning tree T satisfying specified degree restrictions on the vertices. This problem arises naturally in communication networks where the degree of a vertex represents the number of line interfaces available at a terminal (center). The applications of the Degree Constrained Minimum Spanning Tree problems that may arise in real-life include: the design of telecommunication, transportation, and energy networks. It is also used as a subproblem in the design of networks for computer communication, transportation, sewage and plumbing. Since, apart from some trivial cases, the problem is computationally difficult (NP-complete), a number of heuristics have been proposed. In this paper we will discuss the modification of CW1 Algorithm that already proposed by Wamiliana and Caccetta (2003). The results on540 random table problems will be discussed

PERFORMANCE OF THE ACCURACY OF FORECASTING THE CONSUMER PRICE INDEX USING THE GARCH AND ANN METHODS

The Consumer Price Index (CPI) is the most widely used indicator of the inflation rate. Then, the value of CPI in the future must be known to be the basis of the government's making appropriate and accurate policies. The CPI data used in this study was taken from the Central Statistics Agency (BPS) from January 2006 - to December 2021. The CPI data used has a data pattern containing symptoms of heteroskedasticity. To overcome the symptoms of heteroskedasticity, the author uses the GARCH and ANN methods to determine the value of CPI in the future. The GARCH method can overcome the symptoms of heteroskedasticity in the time series forecasting process, while ANN is an effective method in time series forecasting because of its high level of accuracy. In this study, mape error calculation results were obtained with the ARIMA model (4,2,2)~GARCH(1.1) of 3.19% or with an accuracy of 96.81%, and ANN using two hidden layers of 1.24% or with an accuracy of 98.76%. Thus, the results of this study show that the ANN method is the best method of forecasting Consumer Price Index (CPI) data

PENGGUNAAN METODE CUTTING PLANE UNTUK MENYELESAIKAN MINIMUM SPANNING TREE DENGAN KENDALA BOBOT PADA GRAF K_n

This study aims to determine the minimum spanning tree of a complete graph K_n with weight constraints and completion using the cutting plane method. The cutting plane method is one of the algorithms included in the exact method. This algorithm works by reducing the solution area so that it becomes narrower. As a result, the feasible solutions that will be investigated become less and less. This is because the cutting plane method works based on the optimal linear programming solution of relaxation solved by the simplex method. In this paper we give illustration of the algorithm applied for two cases, one for K_4 and one for K_5

The Modified CW1 Algorithm For The Degree Restricted Minimum Spanning Tree Problem

Given edge weighted graph G (all weights are non-negative), The Degree Constrained Minimum Spanning Tree Problem is concerned with finding the minimum weight spanning tree T satisfying specified degree restrictions on the vertices. This problem arises naturally in communication networks where the degree of a vertex represents the number of line interfaces available at a terminal (center). The applications of the Degree Constrained Minimum Spanning Tree problems that may arise in real-life include: the design of telecommunication, transportation, and energy networks. It is also used as a subproblem in the design of networks for computer communication, transportation, sewage and plumbing. Since, apart from some trivial cases, the problem is computationally difficult (NP-complete), a number of heuristics have been proposed. In this paper we will discuss the modification of CW1 Algorithm that already proposed by Wamiliana and Caccetta (2003). The results on540 random table problems will be discussed

Adaptive minimum error least significant bit replacement method for steganography using JPG/JPEG and PNG files

ABSTRACT: Nowadays, the security of data transmission is one of the important aspects in digital data transmission. In this era, sending messages via computers or other gadgets are highly used, the attackers can easily intercept the data during transmission process. Therefore, if there is a secret message, then it can be easily seen. One method for sending data without making curiosity is using the steganography where a secret message can be transmitted in such a way so that attackers are not aware of the existence of something in the message. In this research, we built a digital steganography system using Adaptive Minimum Error Least Significant Bit Replacement (AMELSBR) method. We use .jpg file for hiding the message, .png file for the output, .txt for the message. The procedures for applying AMELSBR method are Capacity Evaluation, Minimum Error Replacement and Error Diffusion. The result shows that the AMELSBR method is able to manage for hiding and restoring files without causing excessive distortion (noise) in stego image, and has a possibility of returning most files for image manipulation such as the change of image brightness and contrast for the black and white color dominan. However, the method is resistant to image cutting (crop)

Modeling and Forecasting by the Vector Autoregressive Moving Average Model for Export of Coal and Oil Data (Case Study from Indonesia over the Years 2002-2017)

The vector autoregressive moving average (VARMA) model is one of the statistical analyses frequently used in several studies of multivariate time series data in economy, finance, and business. It is used in numerous studies because of its simplicity. Moreover, the VARMA model can explain the dynamic behavior of the relationship among endogenous and exogenous variables or among endogenous variables. It can also explain the impact of a variable or a set of variables by means of the impulse response function and Granger causality. Furthermore, it can be used to predict and forecast time series data. In this study, we will discuss and develop the best model that describes the relationship between two vectors of time series data export of Coal and data export of Oil in Indonesia over the period 2002–2017. Some models will be applied to the data: VARMA (1,1), VARMA (2,1), VARMA (3,1), and VARMA (4,1). On the basis of the comparison of these models using information criteria AICC, HQC, AIC, and SBC, it was found that the best model is VARMA (2,1) with restriction on some parameters: AR2_1_2=0, AR2_2_1=0, and MA1_2_1=0. The dynamic behavior of the data is studied through Granger causality analysis. The forecasting of the series data is also presented for the next 12 months. Keywords: VARMA model, Information criteria, Granger causality, Forecasting JEL Classifications: C53, Q4, Q47 DOI: https://doi.org/10.32479/ijeep.760