Desi Rahmadani

Graph labeling is the process of assigning elements from a specific set to the vertices, the edges, or both in a graph. Let G be a graph with vertex set V ( G ), edge set E ( G ), and the number of edges | E ( G )| = q . The graph G is said to be odd harmonious if there exists an injective function g : V ( G ) → 0 , 1 , 2 , … , 2 q − 1 such that the induced mapping g * : E ( G ) → 1 , 3 , 5 , … , 2 q − 1 where g * ( u v ) = g ( u ) + g ( v ) is bijective. Thus, a graph is called odd harmonious if it allows or admits such a labeling. The prism snake graph PS _m is constructed from m copies of the cycle graph C ₄ by connecting three vertices in the same position from two adjacent copies of C ₄ . The generalized chain prism snake graph PS m , n + is a graph constructed from n copies of the chain prism snake graph PS m + by attaching each vertex and edge of two adjacent copies of PS m + . In this research, it will be shown that the prism snake graph PS _m and the generalized chain prism snake graph PS m , n + are odd harmonious graphs, for all m , n ∈ N .

Studi pendahuluan menunjukkan bahwa siswa mengalami kendala menyelesaikan soal cerita Teorema Pythagoras, sehingga perlu adanya analisis secara mendalam. Tujuan penelitian ini untuk menganalisis berbagai kesalahan siswa dalam memecahkan permasalahan soal cerita Teorema Pythagoras. Teori yang digunakan mengacu pada klasifikasi kesalahan menurut Kastolan, yang mengelompokkan kesalahan menjadi tiga bagian, yaitu konseptual, prosedural, dan teknik. Pendekatan yang digunakan yaitu deskriptif kualitatif dengan subjek sebanyak tiga siswa dari kelas VIII di SMP Tamansiswa Kota Malang. Ketiga siswa tersebut dipilih secara purposive sampling dari total 20 siswa yang ada. Instrumen berupa soal tes dan panduan wawancara. Berdasarkan hasil analisis, ditemukan bahwa kesalahan konseptual terjadi karena siswa belum mampu memahami konteks soal dan mengaitkannya dengan konsep dasar Teorema Pythagoras serta melakukan kesalahan dalam menuliskan dan menerapkan rumus. Kesalahan prosedural muncul akibat ketidaktepatan dalam menyelesaikan langkah-langkah perhitungan, seperti tidak menuliskan jawaban akhir sesuai permintaan soal, tidak menyederhanakan bentuk akar, dan kesalahan dalam prosedur penyelesaian. Adapun kesalahan teknik terjadi karena siswa salah dalam menuliskan triple Pythagoras dan keliru dalam melakukan perhitungan kuadrat.

Kegiatan pengabdian ini dilatarbelakangi oleh rendahnya diversifikasi produk dan belum optimalnya pemanfaatan limbah kulit lemon dan kopi pada masyarakat Desa Sumberdem, sehingga potensi ekonomi lokal belum berkembang secara maksimal. Program ini bertujuan meningkatkan kapasitas petani dalam mengolah limbah pertanian menjadi produk bernilai tambah melalui pelatihan destilasi minyak lemon, pembuatan pengharum ruangan berbahan alam, serta pemasaran digital. Metode pelaksanaan menggunakan pendekatan partisipatif melalui tiga tahap kunjungan yang meliputi sosialisasi, demonstrasi, praktik langsung, evaluasi, dan pendampingan pemasaran. Hasil kegiatan menunjukkan bahwa peserta mampu menguasai teknik destilasi sederhana, memproduksi pengharum ruangan secara mandiri, dan mulai memasarkan produk melalui kanal offline maupun digital. Penilaian melalui angket menunjukkan peningkatan pemahaman, keterampilan, dan minat untuk melanjutkan produksi secara berkelanjutan. Program ini menyimpulkan bahwa transfer teknologi sederhana yang disertai pendampingan bertahap efektif dalam mendorong pemanfaatan limbah pertanian, memperkuat kemandirian ekonomi masyarakat, dan membuka peluang pasar bagi produk lokal berkelanjutan.

Graph labeling is one of the significant topics in graph theory. One of its interesting variants is Fibonacci prime labeling, a special type of labeling that assigns Fibonacci numbers as vertex labels while satisfying certain conditions. A graph labeling is an assignment of labels (elements of some set) to elements of a graph, usually the vertices or the edges (or both) of the graph. Several previous studies have shown that some classes of graphs, such as cycle graphs, fan graphs, and umbrella graphs, satisfy the criteria for Fibonacci prime labeling. Moreover, previous research has proven that flower graphs and double flower graphs admit prime labeling. Motivated by these findings, this study aims to explore whether these two classes of graphs also admit Fibonacci prime labeling. This exploration seeks to identify a potential relationship between prime labeling and Fibonacci prime labeling in these graph classes. This research focuses on graphs with an even number of vertices. The methods used include literature review and mathematical proof. The novelty of this study lies in extending the results of prime labeling to Fibonacci prime labeling for flower and double flower graphs. The results show that both graph classes with an even number of vertices belong to the class of graphs that admit Fibonacci prime labeling.

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.

The ability to read and count is essential to be mastered by every student to foster future academic and professional success. However, students with dyslexia have limited ability to read and count. Using learning apps can help children with dyslexia develop reading and counting skills. User interface design is an essential aspect of application development. The research aims to develop a user interface design for learning applications for dyslexic children. User interface design development methods use design thinking approaches that have levels of empathy, define, ideate, prototype, and test. The development of user interface design of learning applications also involves gamification and multi-sensory to help improve students’ understanding of dyslexia when using applications. Evaluation of user interface design using the System Usability Scale (SUS) method yields a total average value of 82. This shows that the user interface design of learning applications for students with dyslexia is acceptable and suitable for users.

Let 𝐹, 𝐺 and 𝐻 be the graphs. We write 𝐹 → (𝐺, 𝐻) if in any red-blue coloring of the edges of 𝐹, there is a red subgraph isomorphic to G or a blue subgra Let 𝐹, 𝐺 and 𝐻 be the graphs. We write 𝐹 → (𝐺, 𝐻) if in any red-blue coloring of the edges of 𝐹, there is a red subgraph isomorphic to G or a blue subgra

An edge-coloring of a graph 𝐺 is called a rainbow if any two vertices are connected by a path of edges of different colors. The strong rainbow connection numbe An edge-coloring of a graph 𝐺 is called a rainbow if any two vertices are connected by a path of edges of different colors. The strong rainbow connection numbe

Let G be a connected and simple graph and Li ⊆ V(G) for all i = 1, 2,., k. For an ordered k – partition ∏={L1,L2,L3,...,Lk} of V(G) and a vertex v ∈ V(G). The r

A decomposition of a graph G is a collection of edge-disjoint subgraphs H1, H2, …, Hr of G such that every edge of G belongs to exactly one Hi. In 2020, Hamilto