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Graph theory as a branch of discrete mathematics has experienced significant development in its application to modern complex network systems, particularly in digital social networks and transportation systems. This research aims to analyze fundamental concepts of graph theory, examine characteristics of cycle detection algorithms along with their computational complexity, investigate their application in digital social network analysis, and explore their implementation in digital transportation system optimization. The research method employs a qualitative approach with library research focusing on scientific literature from 2020-2025 period from accredited academic databases such as Scopus, Web of Science, and IEEE Xplore, utilizing thematic analysis techniques to identify meaningful patterns from the examined literature. Research findings indicate that fundamental graph theory concepts including vertices, edges, and graph classifications form the foundation for relational structure modeling. Cycle detection algorithms such as Depth-First Search, Union-Find, and Tarjan demonstrate effectiveness with O(V+E) complexity for large-scale graphs. Applications in digital social networks facilitate community identification through Multi-View Clustering, centrality analysis for influencer detection, and understanding viral information dissemination patterns. Implementation in digital transportation systems demonstrates route planning optimization using Dijkstra and Bellman-Ford algorithms, vulnerability analysis through articulation point and bridge identification, and bottleneck detection with betweenness centrality. The research concludes that integration of graph theory in discrete mathematics education enhances critical thinking skills and real-world application understanding, with recommendations for algorithm development for massive dynamic graphs and machine learning integration in graph algorithm optimization.

Computational thinking skills are now one of the main skills in 21st century education. Not only does it support mastery of technology, this ability is also very important in understanding and solving problems systematically. This study aims to review in depth the potential for utilizing Triangulos software as an innovative learning medium to improve students' computational thinking skills, especially in mathematical geometry material. The study used a literature review approach by tracing primary and secondary sources from 2020–2024. The results of the analysis show that the use of Triangulos can encourage students to develop algorithmic thinking patterns, spatial visualization, and problem-solving skills. In addition, this application also supports independent and collaborative learning, and has the potential to increase student motivation and activeness in class. These findings recommend the integration of Triangulos in mathematics learning as one of the efforts to innovate education in the digital era. Further empirical research is highly recommended to test the effectiveness of this application at various levels of education.    

The purpose of this study is (1) to describe the characteristics of a good mobile learning application to improve computational thinking and learning independence of high school students. (2) to produce a mobile learning application that is oriented towards computational thinking skills and student learning independence with good quality. The quality of the development results is determined based on Nieveen's criteria, namely valid, practical, and effective. This study is a research and development (R&D) that uses the Borg & Gall development model with 8 development steps, namely preliminary study, planning, initial product development, small group trials, main product revision, limited scale trials, operational product revisions and large-scale trials. The subjects in this study were 36 students from one class at SMA Negeri 1 Gamping, Sleman Regency. The instrument used to measure the validity of the mobile learning application is the expert validation sheet. The instrument to measure the practicality of the mobile learning application is the student response questionnaire. The instrument to measure the effectiveness of the application is the computational thinking test and the student learning independence questionnaire. Validity and practicality data analysis was conducted by converting quantitative data into qualitative form in the form of four standard scale values, while effectiveness data analysis based on test and questionnaire results was conducted using paired sample t-test. The results of the study showed that (1) Mobile learning applications have the characteristics of being easy to apply, flexible to time, lightweight and easy to carry anywhere and also implementing each computational thinking indicator in each stage of the material. (2) The results of expert validation showed that the developed mobile learning application met the valid criteria as seen by the Aiken's validity test score for media experts of 0.83 and 0.68 for material experts. The practicality of the mobile learning application is included in the very good category as seen from the average results with an average percentage of student responses of 87.17%. The effectiveness of the computational thinking test obtained a t-value of 47.22 greater than t (35,0.05) with a score of 1.69, the effectiveness of the learning independence test based on the t test obtained a t-value of 4.85 greater than t (35,0.05) with a score of 1.69. Based on the results obtained, it can be concluded that the developed mobile learning application meets the criteria of validity, practicality and effectiveness.

Computational thinking is the ability to solve problems and design systems using concepts and techniques generally associated with computers and computer programming. The aim of this research is to conduct a literature review, namely to determine the application of computational thinking in mathematics learning. The technique used is the Systematic Literature Review (SLR) strategy. SLR is a research method that aims to identify, study and interpret data in journals systematically with specified stages. The conclusion obtained from the research results is that the application of computational thinking in mathematics learning can be done using four foundations of computational thinking, namely: (1) Decomposition, namely the problem is divided into small parts, (2) Pattern recognition, namely the process of identifying patterns or sequences of problems, (3) Abstraction, namely consideration of the important parts of a problem, and (4) Algorithm, namely a series of instructions for solving the problem. Examples of its application include the use of interactive mathematics software, mathematical simulations, problem-based learning with technology, adaptive learning and the use of educational games.  

This literature study analysis discusses improving computational thinking problem solving abilities in madrasah ibtidaiyah students. In this study, an analysis of various literature that has been carried out previously was carried out to understand how the use of computational thinking can improve problem solving abilities in madrasah ibtidaiyah students. One of the journals that is relevant to this topic is "Computational Thinking in Madrasah Tsanawiyah Maulana Maghribi Kandeman Students in Improving Problem Solving Abilities" which was published in the journal Circle: Journal of Mathematics Education. This journal was written by Muhammad Nur Fain Syamsy and A. Sholikhah on September 28 2023. This study explores how the application of computational thinking can help students solve problems. The research results show that students who are involved in learning computational thinking have better problem solving abilities. Apart from that, other relevant research is research conducted by Kurnadi et al. (2021) which concerns the introduction of computational thinking to students at Madrasah Ibtidaiyah Nahdlatul Wathan Marcapada West Lombok. This research also shows that learning computational thinking can improve students' problem solving abilities. In this research, the use of literature study analysis methods is important to gain a deep understanding of the influence of computational thinking on problem-solving abilities in madrasah ibtidaiyah students. By studying existing literature, researchers can identify the best approaches and strategies in developing students' problem solving abilities.