On the Relation of the Total Graph of a Ring and a Product of Graphs

The total graph of a ring R, denoted as T(Γ(R)), is defined to be a graph with vertex set V(T(Γ(R)))=R and two distinct vertices u,v∈V(T(Γ(R))) are adjacent if and only if u+v∈Z(R), where Z(R) is the zero divisor of R. The Cartesian product of two graphs G and H is a graph with the vertex set V(G×H)=V(G)×V(H) and two distinct vertices (u_1,v_1 ) and (u_2,v_2 ) are adjacent if and only if: 1) u_1=u_2 and v_1 v_2∈H; or 2) v_1=v_2 and u_1 u_2∈E(G). An isomorphism of graphs G dan H is a bijection ϕ:V(G)→V(H) such that u,v∈V(G) are adjacent if and only if f(u),f(v)∈V(H) are adjacent. This paper proved that T(Γ(Z_2p )) and P_2×K_p are isomorphic for every odd prime p

Jelajah judul skripsi UIN Maliki

Platform verifikasi judul skripsi yang dirancang untuk Program Studi Matematika UIN Maulana Malik Ibrahim Malang ini menawarkan fitur penting yang memungkinkan mahasiswa untuk memastikan keunikan judul karya ilmiah mereka. Menggunakan algoritma Jarak Levenshtein yang canggih, sistem ini secara otomatis membandingkan judul yang diusulkan dengan database ekstensif yang berisi judul skripsi yang telah disetujui. Keakuratan analisis ini disediakan oleh metrik kemiripan yang dihasilkan, yang secara intuitif menunjukkan tingkat kesesuaian judul yang diajukan terhadap yang telah ada. Fitur ini secara efektif meminimalkan risiko penolakan judul karena duplikasi, dan mendukung upaya mahasiswa dalam menciptakan judul yang inovatif dan asli

Solusi sistem persamaan linier

Program ini dapat digunakan untuk mencari solusi numerik sistem persamaan linie

Visualisasi dan penyelesaian pemrograman linier dengan metode grafik

Program ini digunakan sebagai media pembelajaran dalam menentukan solusi masalah pemrograman linier dengan menggunakan metode grafik. Tidak hanya sebagai media pembelajaran, program ini juga dapat digunakan untuk mencari solusi permasalahan pemrograman linier yang disyaratkan, yaitu terdiri dari dua variabel

Visualisasi pencarian solusi sistem persamaan linier dua dan tiga variabel

Program ini digunakan sebagai media pembelajaran dalam menentukan solusi sistem persamaan linier dua dan tiga variabel. Tidak hanya sebagai media pembelajaran, program ini juga dapat digunakan untuk mencari solusi SPL yang disyaratkan, yaitu terdiri dari dua atau tiga variabel

Agglomerative hierarchical clustering analysis based on partially-ordered Hasse Graph of poverty indicators in East Java

Poverty is a central issue in many countries, so one of the main goals of a country is to eradicate poverty. One of the efforts is to identify indicators that affect poverty using cluster analysis. In this research, we discuss cluster analysis using the agglomerative hierarchical clustering method based on the partially-ordered Hasse graph. Meanwhile, one form of facilitating cluster analysis is the Hasse graph. Therefore, this study was conducted to find out which areas have close or similar poverty indicators based on the partially-ordered Hasse graph and reduce the incidence of poverty in East Java. Before conducting cluster analysis, a multicollinearity test was carried out between poverty indicators, then the proximity between objects was determined using the Euclidean distance. Afterward, cluster analysis was performed using agglomerative methods (single linkage and complete linkage) to obtain the best cluster solution. The single linkage method provides the best solution consisting of five clusters. The results of the partially-ordered Hasse graph show that the fifth cluster becomes the top layer based on the Gini indicator. The fourth cluster becomes the top layer based on the depth index indicator. Last, the first cluster becomes the top layer based on the open unemployment rate indicator and life expectancy

Agglomerative hierarchical clustering analysis based on partially-ordered Hasse Graph of poverty indicators in East Java

Poverty is a central issue in many countries, so one of the main goals of a country is to eradicate poverty. One of the efforts is to identify indicators that affect poverty using cluster analysis. In this research, we discuss cluster analysis using the agglomerative hierarchical clustering method based on the partially-ordered Hasse graph. Meanwhile, one form of facilitating cluster analysis is the Hasse graph. Therefore, this study was conducted to find out which areas have close or similar poverty indicators based on the partially-ordered Hasse graph and reduce the incidence of poverty in East Java. Before conducting cluster analysis, a multicollinearity test was carried out between poverty indicators, then the proximity between objects was determined using the Euclidean distance. Afterward, cluster analysis was performed using agglomerative methods (single linkage and complete linkage) to obtain the best cluster solution. The single linkage method provides the best solution consisting of five clusters. The results of the partially-ordered Hasse graph show that the fifth cluster becomes the top layer based on the Gini indicator. The fourth cluster becomes the top layer based on the depth index indicator. Last, the first cluster becomes the top layer based on the open unemployment rate indicator and life expectancy

Survey on topological indices and graphs associated with a commutative ring

The researches on topological indices are initially related to graphs obtained from biological activities or chemical structures and reactivity. Recently, the research on this topic has evolved on graphs in general and even on graphs obtained from algebraic structures, such as groups, rings or modules. This paper will present various topological index concepts, various graph concepts obtained from a commutative ring and some previous studies that are relevant to those two concepts. Based on the various concepts presented, research topics related to topological indices of a graph associated with a commutative ring can be found and carried out

Implementasi algoritma A-Star dalam menentukan rute terpendek destinasi wisata Kota Malang

INDONESIA: Berwisata menjadi salah satu kebutuhan setiap orang untuk merelaksasikan pikiran dari kesibukan yang dijalani di setiap harinya. Salah satu kota di Jawa Timur yang menjadi tempat primadona untuk berwisata adalah Kota Malang. Kota ini memiliki kurang lebih 43 destinasi wisata. Biasanya wisatawan yang ingin berkunjung tidak hanya ke salah satu tempat, namun beberapa tempat. Akibatnya dibutuhkan sebuah bantuan untuk menentukan destinasi mana saja yang harus dikunjungi terlebih dahulu agar perjalanan berwisata mereka menjadi efektif. Proses pencarian rute terpendek pada penelitian ini menggunakan Algoritma A-Star, salah satu algoritma BFS yang dalam prosesnya sangat mempertimbangkan nilai heuristik. Proses pengujian rute terpendek dilakukan dengan memilih titik awal, kemudian memilih beberapa lokasi wisata. Selanjutnya akan dicari rute terpendek menggunakan algoritma A-star pada setiap destinasi, kemudian dipilih destinasi mana yang akan dikunjungi pertama. Begitu pun seterusnya sampai destinasi terakhir. Keefektifan rute melibatkan perbandingan dengan rute yang disajikan oleh Google maps. Berdasarkan hasil 30 kali percobaan pada beberapa destinasi yang bersifat menyeluruh, didapatkan hasil bahwa rata-rata pencarian rute menggunakan algoritma A-Star adalah 44,17% lebih pendek dibandingkan yang tersaji pada google maps. Hal ini dikarenakan keunikan dari algoritma di mana terdapat nilai heuristik dan penyeleksian pada tiap destinasi sehingga menjadikan rute lebih efektif. ENGLISH: Traveling is one of the needs of everyone to relax the mind from the busyness that is lived every day. One of the cities in East Java which is a prima donna for traveling is Malang. The city has approximately 43 tourist destinations. Usually, tourists who want to visit not only one place, but several places. generate assistance in deciding which destinations to visit first in order for their trip to be effective. The shortest search process in this study uses the A-Star Algorithm, one of the BFS algorithms which in the process really considers the heuristic value. The process of testing the shortest route is done by selecting a starting point, then selecting several tourist locations. Next, the shortest route will be searched using the A-star algorithm at each destination, then which destination will be visited first. And so on until the final destination. The effectiveness of the route which involves comparison with the route presented by google maps. Based on the results of 30 experiments on several comprehensive destinations, it was found that the average route search using the A-Star algorithm was 44.17% shorter than that presented on google maps. This is due to the uniqueness of the algorithm in which there is a heuristic value and selection for each destination so as to make the route more effective

Color laplacian and color signless laplacian energy of complement of subgroup graph of dihedral group

Laplacian and signless laplacian energy of a finite graph is the most interesting topics on areas of energy of a graph. The new concept of energy of a graph is color energy and furthermore color laplacian and color signless laplacian energy. In this paper, the formulae of color laplacian and color signless laplacian energy of complement of subgroup graphs of dihedral group are determined. Color laplacian and color signless laplacian spectrum of these graphs are also computed