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Journal : Science and Technology Indonesia

Enumerate the Number of Vertices Labeled Connected Graph of Order Seven Containing No Parallel Edges Muslim Ansori; Wamiliana; Fitriani; Yudi Antoni; Desiana Putri
Science and Technology Indonesia Vol. 7 No. 3 (2022): July
Publisher : Research Center of Inorganic Materials and Coordination Complexes, FMIPA Universitas Sriwijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (744.732 KB) | DOI: 10.26554/sti.2022.7.3.392-399

Abstract

A graph that is connected G(V,E) is a graph in which there is at least one path connecting every two vertices in G; otherwise, it is called a disconnected graph. Labels or values can be assigned to the vertices or edges of a graph. A vertex-labeled graph is one in which only the vertices are labeled, and an edges-labeled graph is one in which only edges are assigned values or labels. If both vertices and edges are labeled, the graph is referred to as total labeling. If given n vertices and m edges, numerous graphs can be made, either connected or disconnected. This study will be discussed the number of disconnected vertices labeled graphs of order seven containing no parallel edges and may contain loops. The results show that number of vertices labeled connected graph of order seven with no parallel edges is N(G7,m, g)l= 6,727×Cm6; while for 7≤g≤ 21, N(G7,m, g)l= kg C(m−(g−6))g−1, where k7 =30,160, k8 = 30,765, k9=21,000, k10 =28,364, k11= 26,880, k12=26,460 , k13 = 20,790, k14 =10,290, k15 = 8,022, k16 = 2,940, k17 =4,417, k18 = 2,835, k19 =210, k20 = 21, k21= 1.
The Diameter and Maximum Link of the Minimum Routing Cost Spanning Tree Problem Reni Permata Sari; Wamiliana; Akmal Junaidi; Wiwin Susanty
Science and Technology Indonesia Vol. 7 No. 4 (2022): October
Publisher : Research Center of Inorganic Materials and Coordination Complexes, FMIPA Universitas Sriwijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (856.521 KB) | DOI: 10.26554/sti.2022.7.4.481-485

Abstract

The minimum routing cost spanning tree (MRCST) is a spanning tree that minimizes the sum of pairwise distances between its vertices given a weighted graph. In this study, we use Campos Algorithm with slight modifications on the coefficient of spanning potential. Those algorithms were implemented on a random table problem data of complete graphs of order 10 to 100 in increments of 10. The goal is to find the diameter (the largest shortest path distance) and the maximum link (the maximum number of edges connecting two vertices) in the spanning tree solution of MRCST. The result shows that a slight modification of the spanning potential coefficients gives better solutions.
Enumerating the Number of Connected Vertices Labeled Graph of Order Six with Maximum Ten Loops and Containing No Parallel Edges Wamiliana Wamiliana; Amanto Amanto; Mustofa Usman; Muslim Ansori; Fadila Cahya Puri
Science and Technology Indonesia Vol. 5 No. 4 (2020): October
Publisher : Research Center of Inorganic Materials and Coordination Complexes, FMIPA Universitas Sriwijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (2285.683 KB) | DOI: 10.26554/sti.2020.5.4.131-135

Abstract

A Graph G (V, E) is said to be a connected graph if for every two vertices on the graph there exist at least a path connecting them, otherwise, the graph is disconnected. Two edges or more that connect the same pair of vertices are called parallel edges, and an edge that starts and ends at the same vertex is called a loop. A graph is called simple if it containing no loops nor parallel edges. Given n vertices and m edges, m ≥ 1, there are many graphs that can be formed, either connected or disconnected. In this research, we will discuss how to calculate the number of connected vertices labeled graphs of order six (isomorphism graphs are counted as one), with a maximum loop of ten without parallel edges.
Determining The Number of Connected Vertex Labeled Graphs of Order Seven without Loops by Observing The Patterns of Formula for Lower Order Graphs with Similar Property Muslim Ansori; Wamiliana; Fadila Cahya Puri
Science and Technology Indonesia Vol. 6 No. 4 (2021): October
Publisher : Research Center of Inorganic Materials and Coordination Complexes, FMIPA Universitas Sriwijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26554/sti.2021.6.4.328-336

Abstract

Given n vertices and m edges, m ≥ 1, and for every vertex is given a label, there are lots of graphs that can be obtained. The graphs obtained may be simple or not simple, connected or disconnected. A graph G(V,E) is called simple if G(V,E) not containing loops nor paralel edges. An edge which has the same end vertex is called a loop, and paralel edges are two or more edges which connect the same set of vertices. Let N(G7,m,t) as the number of connected vertex labeled graphs of order seven with m vertices and t (t is the number edges that connect different pair of vertices). The result shows that N(G7,m,t) = ct C (m−1) t−1, with c6=6727, c7=30160 , c8=30765, c9=21000, c10=28364, c11=26880, c12=26460, c13=20790, c14=10290, c15= 8022, c16=2940, c17=4417, c18=2835, c19=210, c20= 21, c21=1.
Dynamic Modeling and Forecasting Data Energy Used and Carbon Dioxide (CO2) Edwin Russel; Wamiliana; Nairobi Saibi; Warsono; Mustofa Usman; Jamal I. Daoud
Science and Technology Indonesia Vol. 7 No. 2 (2022): April
Publisher : Research Center of Inorganic Materials and Coordination Complexes, FMIPA Universitas Sriwijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1425.261 KB) | DOI: 10.26554/sti.2022.7.2.228-237

Abstract

The model of Vector Autoregressive (VAR) with cointegration is able to be modified by Vector Error Correction Model (VECM). Because of its simpilicity and less restrictions the VECM is applied in many studies. The correlation among variables of multivariate time series also can be explained by VECM model, which can explain the effect of a variable or set of variables on others using Granger Causality, Impulse Response Function (IRF), and Forecasting. In this study, the relationship of Energy Used and CO2 will be discussed. The data used here were collected over the year 1971 to 2018. Based on the comparison of some criteria: Akaike Information Criterion Corrected (AICC), Hannan-Quin Information Criterion (HQC), Akaike Information Criterion (AIC) and Schwarz Bayesian Criterion (SBC) for some VAR(p) model with p= 1,2,3,4,5, the best model with smallest values of AICC, HQC, AIC and SBC is at lag 2 (p= 2). Then the best model found is VECM (2) and further analysis such as Granger Causality, IRF, and Forecasting will be based on this model.
Analysis Multivariate Time Series Using State Space Model for Forecasting Inflation in Some Sectors of Economy in Indonesia Edwin Russel; Wamiliana Wamiliana; Warsono; Nairobi; Mustofa Usman; Faiz AM Elfaki
Science and Technology Indonesia Vol. 8 No. 1 (2023): January
Publisher : Research Center of Inorganic Materials and Coordination Complexes, FMIPA Universitas Sriwijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26554/sti.2023.8.1.144-150

Abstract

Many analytical methods can be utilized for multivariate time series modeling. One of the analytical models for modeling time series data with multiple variables is the State Space Model. The data to be analyzed in this study is inflation data from expenditure groups such as processed foods, beverages, cigarettes, and tobacco; and housing inflation for water, electricity, gas, and fuel from January 2001 to December 2021. The aim is to determine the best State Space Model that fits the data for forecasting. In this study, the State Space method will be utilized further with multivariate time series data and represent State Space in Vector Autoregressive (VAR) to determine the relationship between groups of observed variables.
The Relationship of Multiset, Stirling Number, Bell Number, and Catalan Number Wamiliana; Attiya Yuliana; Fitriani
Science and Technology Indonesia Vol. 8 No. 2 (2023): April
Publisher : Research Center of Inorganic Materials and Coordination Complexes, FMIPA Universitas Sriwijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26554/sti.2023.8.2.330-337

Abstract

Catalan numbers is not as famous as Fibonacci numbers, however this number has own its beauty and arts. Catalan numbers was discovered by Ming Antu in 1730, however, this numbers is credited to Eugene Catalan when he was studying parentheses in 1838. Catalan numbers mostly occurs in counting or enumeration problems. The Catalan numbers can be defined in more than one forms, and the most famous form is Cn = 1/n+1(2nn). In this study we will discuss the multiset construction and the relationship of the results of Multiset with Stirling, Bell, and Catalan numbers.
Solving the Shortest Total Path Length Spanning Tree Problem Using the Modified Sollin and Modified Dijkstra Algorithms Wamiliana; Reni Permata Sari; Astri Reformasari; Jani Suparman; Akmal Junaidi
Science and Technology Indonesia Vol. 8 No. 4 (2023): October
Publisher : Research Center of Inorganic Materials and Coordination Complexes, FMIPA Universitas Sriwijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26554/sti.2023.8.4.684-690

Abstract

In a weighted connected graph, the shortest total path length spanning tree problem is a problem when we need to discover the spanning tree with the lowest total cost of all pairwise distances between its vertices. This problem is also known as the minimum routing cost spanning tree (MRCST). In this study, we will discuss the Modified Sollin and Modified Dijkstra Algorithms to solve that problem which implemented on 300 problems are complete graphs of orders 10 to 100 in increments of 10, where every order consists of 30 problems. The results show that the performance of the Modified Dijkstra and the Modified Sollin Algorithms are slightly similar. On orders 10, 20, 30, 60, and 80, the Modified Dijkstra Algorithm performs better than the Modified Sollin, however on orders 40, 50, 70, 90, and 100, the Modified Sollin performs better.