Vita Kusumasari

Graph labeling is the assigning of labels represented by integers or symbols to graph elements, edges and/or vertices (or both) of a graph. Consider a simple graph with a vertex-set and an edge-set . The order of graph , denoted by , is the number of vertices on . The prime labeling is a bijective function , such that the labels of any two adjacent vertices in G are relatively prime or , for every two adjacent vertices and in . If a graph can be labeled with prime labeling, then the graph can be said to be a prime graph. A flower graph is a graph formed by helm graph by connecting its pendant vertices (the vertices have degree one) to the central vertex of , such a flower graph is denoted as In this research, we employ constructive and analytical methods to investigate prime labelings on specific graph classes. Definitions, lemmas, and theorems are developed as the main results in this research. The amalgamation is a graph formed by taking all by taking all the and identifying their fixed vertices . If , then we write with . In previous research, it has been shown that the flower graphs , for are prime graphs. Continuing the research, we prove that two classes of amalgamation of flower graphs are prime graphs.

Mental models are internal representations students form about a concept, which can be inferred through their external representations. This study aims to describe the characteristics of junior high school students' formal mental models in understanding the concept of integers. Conducted in a class of 44 seventh-grade students, this qualitative study employed a case study methodology. Subjects were selected using a purposive sampling, with two subjects chosen for in depth exploration and interviews. Data were analyzed using the Miles and Huberman model, encompassing data condensation, data presentation, and conclusion drawing. The results revealed that the students at the formal mental model level demonstrated the characteristics of being able to place positive integers, zero, and negative integers on a number line, compare positive and negative integers, compare two negative integers, sort integers, add and subtract integers, and sort them accordingly. By refining the characteristics of mental models of value and order of integers, and integrating Bofferding's ideas on the mental model of value and order of integers and mental model of directed magnitude, this study successfully expands the theoretical framework of students' mental models in understanding the concept of integers, extending it to include addition and subtraction operations. Practically, it provides educators with insights into the characteristics of formal mental models that seventh-grade students need to master, supporting the development of meaningful instructional strategies to strengthen students’ conceptual understanding and promote the advancement of mental models to the formal level. In addition, these findings serve as a reference for future research on students' mental models in understanding integers and performing integer operations. Abstrak Model mental diartikan sebagai representasi internal yang dimiliki siswa mengenai suatu konsep yang kemudian dapat diketahui melalui representasi eksternal. Penelitian ini bertujuan untuk mendeskripsikan karakteristik model mental formal siswa SMP dalam memahami konsep bilangan bulat. Penelitian ini dilakukan di kelas VII SMP yang terdiri dari 44 siswa. Metode penelitian yang digunakan adalah kualitatif dengan jenis penelitian studi kasus. Pemilihan subjek menggunakan teknik purposive sampling, yakni terdapat 2 subjek untuk dieksplorasi dan diwawancarai. Teknik analisis data menggunakan model Miles dan Huberman meliputi kondensasi data, penyajian data, dan penarikan kesimpulan. Hasil penelitian menunjukkan bahwa karakteristik siswa pada level model mental formal adalah dapat menempatkan bilangan bulat positif, nol, dan bilangan bulat negatif pada garis bilangan, dapat membandingkan bilangan bulat positif dan bilangan bulat negatif, dapat membandingkan dua bilangan bulat negatif, dapat mengurutkan bilangan bulat, dapat menjumlahkan dan mengurangkan bilangan bulat sekaligus mengurutkannya. Dengan mempertajam karakteristik model mental nilai dan urutan bilangan bulat, serta mengintegrasikan gagasan Bofferding tentang model mental nilai dan urutan bilangan bulat dan model mental besaran terarah, penelitian ini berhasil memperluas kerangka teori tentang model mental siswa dalam memahami konsep bilangan bulat, sehingga mencakup pula operasi penjumlahan dan pengurangan. Secara praktis, studi ini memberikan wawasan kepada pendidik mengenai karakteristik model mental formal yang perlu dikuasai oleh siswa kelas tujuh, mendukung pengembangan strategi pengajaran yang bermakna untuk memperkuat pemahaman konseptual siswa dan mendorong perkembangan model mental mereka ke tingkat formal. Selain itu, temuan ini dapat dijadikan acuan untuk penelitian lebih lanjut mengenai model mental siswa dalam memahami bilangan bulat dan melakukan operasi bilangan bulat.

Data containing spatial effects should be analyzed using a spatial model. One of the spatial models is Spatial Durbin Error Model (SDEM). In the SDEM model, the independent variable and error both contain spatial effects. Along with the implementation of regional autonomy, each region is given the freedom to regulate financing. Each area tries to explore their respective potential to get a large Regional Original Income. Taxes are an essential source of the regional revenue so that local governments try to optimize tax revenue. This paper empirically examines the factors that can maximize tax revenue in East Java and maps the potential areas to generate high taxes. Some of the factors considered include Gross Regional Domestic Product (GRDP), population, per capita income, number of industries. By using the SDEM model, it can be seen that there is a spatial relationship, where the amount of tax revenue in each region is different and is influenced by other areas.

The Hyperbolic MBO (HMBO) algorithm has been modified to handle the problem of obstacle. In this paper, we use this algorithm to simulate the movement of interface regarding the curvature dependent acceleration. The initial curve and the obstacle are considered as closed curves. The obstacle is placed within the initial curve. We examine the curve movement. In the obstacle problem, we obtain that the curve movement does not exceed the obstacle. After touching the obstacle, the curve attaches to it.

The previous single element antenna was made of two separated layers, one for the patch antenna (upper) and the other for the feed-line (below), using proximity feed for a thin configuration. In this time, a novel dual feed antenna with a hole-truncated is proposed for the generation of a compact LHCP (Left Handed Circular Polarization) using a compact equilateral triangular-patch antenna, that one of the microstrip-line feeds is longer than the other for introducing a 90° phase delay. The influence of the hole-truncated that embedded on the patch is investigated to make the patch antenna smaller than the previous antenna. The method of moments (IE3D Zeland Software) is used considering a finite ground analysis. The simulation results show that the patch length decreases by 12.65 % (a = 52.80 mm to a = 46.12 mm) with a gain and axial ratio at 2.5025 GHz being 6.82 dBic and 0.66 dB, respectively. The bandwidth of the hole-truncated antenna, by comparison of the previous antenna is smaller.

At the firstly single element of the singly fed pentagonal patch antenna using air gap is proposed. The results show that the bandwidth of impedance axial ratio and gain at the resonant frequency 2.4925 GHz are 15.67 %, 4.11 % and 52.16 %, respectively. Moreover the value of S-parameter axial ratio and gain at 2.4925 GHz are -15.03 dB, 0.06 dB and 8.74 dBic, respectively. Furthermore in this research it is also investigated circularly polarized array pentagonal microstrip antenna for mobile satellite communications especially to enhance the bandwidth axial ratio that are examined both of simulation and measurement. The results of array pentagonal patch antenna is similar with its single especially the value of S-parameter axial ratio and gain as the mentioned above. The other results related the simulation show that the cutting of beam angle between of them is the same. In case of measurement results owing to loss during measuring the gain decreasing and affect the cutting of beam angle between gain and axial ratio that is not satisfied yet.