Banyak Pohon Pembangun pada Graf Barbell

Teori graf merupakan salah satu bidang ilmu yang memiliki berbagai kegunaan dalam kehidupan sehari-hari. Salah satu topik yang dibahas dalam teori graf yaitu terkait banyak pohon pembangun (Spanning Trees). Pohon (Tree) dalam teori graf merupakan suatu graf terhubung yang tidak memuat cycle. Kemudian banyak pohon pembangun (spanning trees) dari suatu graf terhubung didefinisikan sebagai banyaknya pohon yang dapat dibentuk dari suatu graf yang melewati semua simpul pada graf tersebut. Pada penelitian ini, akan dibahas terkait spanning trees atau pohon pembangun dari graf barbell. Graf Barbell  merupakan graf yang diperoleh dengan menghubungkan  buah graf lengkap  oleh sebuah bridge. Berdasarkan hasil penelitian dari artikel ini diperoleh suatu fakta bahwa graf barbell  memiliki spanning trees sebanyak . Selanjutnya pada artikel ini juga akan dibahas terkait beberapa sifat dari spanning trees dan graf barbell

Analisis Masalah Heteroskedastisitas Menggunakan Generalized Least Square dalam Analisis Regresi

Regression analysis is one statistical method that allows users to analyze the influence of one or more independent variables (X) on a dependent variable (Y).The most commonly used method for estimating linear regression parameters is Ordinary Least Square (OLS). But in reality, there is often a problem with heteroscedasticity, namely the variance of the error is not constant or variable for all values of the independent variable X. This results in the OLS method being less effective. To overcome this, a parameter estimation method can be used by adding weight to each parameter, namely the Generalized Least Square (GLS) method. This study aims to examine the use of the GLS method in overcoming heteroscedasticity in regression analysis and examine the comparison of estimation results using the OLS method with the GLS method in the case of heteroscedasticity.The results show that the GLS method was able to maintain the nature of the estimator that is not biased and consistent and able to overcome the problem of heteroscedasticity, so that the GLS method is more effective than the OLS method

Analisis Rotasi Ortogonal pada Teknik Analisis Faktor Menggunakan Metode Procrustes

Factor analysis is a multivariate statistical method that tries to explain the relationship between a number of independent variables by grouping these variables into factors. With this grouping, the existing variables will be easier to interpret. In increasing the power of factor interpretation, a matrix loading factor transformation must be performed. The transformation can be done by choosing the method that is in orthogonal rotation, the varimax or quartimax or equamax method. In order to find out which rotation techniques is the most appropriate, the minimum square distance values () generated from the procrustes method used. In this study three data were used from the results of the questionnaire, for data I obtain the value of the minimum distance squared with a varimax rotation that is  with ; for data II obtain the value of the minimum distance squared with a quartimax rotation that is  with ; for data III obtain the value of the minimum distance squared with a varimax rotation that is  with

Ekivalensi Ideal Hampir Prima dan Ideal Prima pada Bilangan Bulat Gauss

Kriptografi adalah salah satu cabang ilmu matematika yang banyak digunakan pada sistem keamanan digital. Kriptografi itu sendiri berkaitan dengan bilangan bulat dan sifat-sifatnya, terutama bilangan prima. Lebih spesifik, beberapa algoritma penting seperti RSA, sangat bergantung pada faktorisasi prima dari bilangan bulat. Abstraksi bilangan prima diperkenalkan oleh Dedekind pada tahun 1871, dikenal dengan nama ideal prima. Ideal prima diperumum oleh Bhatwadekar pada tahun 2009 dan dinamakan ideal hampir prima. Paper ini akan membuktikan bahwa ideal hampir prima dan ideal prima di bilangan bulat Gasuss adalah ekivale

Analisis Automorfisma Graf Pembagi-nol dari Ring Komutatif dengan Elemen Satuan

Zero-divisor graphs of a commutative ring with identity has 3 specific simple forms, namely star zero-divisor graph, complete zero-divisor graph and complete bipartite zero-divisor graph. Graph automorphism is one of the interesting concepts in graph theory. Automorphism of  graph G is an isomorphism from graph G to itself. In other words, an automorphism of a graph G is a permutation φ of  the set points V(G) which has the property that (x,y) in E(G)  if and only if (φ(x),φ(y)) in E(G), i.e. φ preserves adjacency.This study aims to analyze the form of zero-divisor graph automorphisms of a commutative ring with identity formed. The method used in this study was taking sampel of each zero-divisor graph to represent each graph. Thus, pattern and shape of automorphism of each graph can be determined. Based on the results of this study, a star zero-divisor graph with pattern K_1,(p-1), where p is prime, has (p-1)! automorphisms, a complete zero-divisor graph with pattern K_(p-1), where p is prime, has (p-1)!  automorphisms, and a complete bipartite zero-divisor graph with pattern K_(p-1),(q-1), where p is prime, has (p-1)!(q-1)! automorphisms, when p not equals to q  and 2((p-1)!(q-1)!) automorphisms  when p=q

Analisis Keberhinggaan Matriks Representasi atas Grup Berhingga

Representation of a finite group G over generator linear non singular mxm matrix with entries of field K defined by group homomorphismA : G → GLm(K)Basically, the non singular mxm matrix A(x) which representing the finite group G divided into two, that are the unitary matrix and non unitary matrix . If A(x) is a non unitary matrix, then there exist a unitary matrix which similar to A(x). This research deals to analyze the numbers of one example of a unitary matrix representation over arbitrary finite group G with order n that is permutation matrix, and the number of unitary matrix which is similar to real non unitary matrix representation of arbitrary finite group G order 2. The results showed the numbers of permutation matrix representation is n! and unitary matrix which is similar to non unitary matrix representation is 2

The Power Graph of a Dihedral Group

Graph theory is one of the topics in mathematics that is quite interesting to study because it is applicable and can be combined with other mathematical topics such as group theory. The combination of graph theory and group theory is that graphs can be used to represent a group. An example of a graph is a power graph. A power graph of the group  is defined as a graph whose vertex set is all elements of  and two distinct vertices  and  are connected if and only if  or for a positive integer x and y. In this study, the author discusses the power graph of the dihedral group  The results obtained from this study are the power graph of the dihedral group  where  with  prime numbers and an  natural number is a graph consisting of two non-disjoint subgraphs, namely complete subgraphs and star subgraphs. And we find that its radius and diameter are 1 and 2

SOME PROPERTIES OF COPRIME GRAPH OF DIHEDRAL GROUP D_2n WHEN n IS A PRIME POWER

The Study of algebraic structures, especially on graphs theory, leads to anew topics of research in recent years. In this paper, the algebraic structures that will be represented by a coprime graph are the dihedral group and its subgroups. The coprime graph of a group G, denoted by \Gamma_D_2n is a graph whose vertices are elements of G and two distinct vertices a and b are adjacent if only if (|a,|b|)=1. Some properties of the coprime graph of a dihedral group D_2n are obtained. One of the results is if n is prime then \Gamma_D_2n is a complete bipartite graph. Moreover, if n is the power of prime then \Gamma_D_2n is a multipartite graph

COPRIME GRAPH OF INTEGERS MODULO n GROUP AND ITS SUBGROUPS

Coprime Graph is a geometric representation of a group in the form of undirectedgraph. The coprime graph of a group G, denoted by $\Gamma_G$ is a graph whose vertices are all elements of group G; and two distinct vertices a and b are adjacent if and only if $(|a|,|b|)=1$. In this paper, we study coprime graph of integers modulo n group and its subgroups. One of the results is if n is a prime number, then coprime graph of integers modulo n group is a bipartite graph

SOME RESULT OF NON-COPRIME GRAPH OF INTEGERS MODULO n GROUP FOR n A PRIME POWER

One interesting topic in algebra and graph theory is a graph representation of a group, especially the representation of a group using a non-coprime graph.  In this paper, we describe the non-coprime graph of integers modulo  group and its subgroups, for  is a prime power or  is a product of two distinct primes