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All Journal Kubik KUBIK: Jurnal Publikasi Ilmiah Matematika Jurnal Matematika dan Sains (JMS)
Nursyahida, Salwa
UIN Sunan Gunung Djati Bandung
Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Chemistry Computer Science & IT Economics, Econometrics & Finance Education Mathematics Physics

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Journal : Kubik

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A Collection of Minimally Path Square-Saturated Graphs Salwa Nursyahida
KUBIK Vol 5, No 1 (2020): KUBIK: Jurnal Publikasi Ilmiah Matematika
Publisher : Jurusan Matematika, Fakultas Sains dan Teknologi, UIN Sunan Gunung Djati Bandung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15575/kubik.v5i1.8415

Abstract

Given a simple graph G, m a positive integer. The square of path graph P_m, denoted by P_m^2, is a graph obtained from P_m by adding new edges between any pair of vertices at distance at most 2 in P_m. A graph G is P_m^2-saturated if G does not contain P_m^2 as a subgraph, but the addition of any edge between two nonadjacent vertices in G contain P_m^2. The minimum size of P_m^2-saturated graph on n vertices is called a saturation number for P_m^2, denoted by sat(n,P_m^2). A set Sat(n,P_m^2 )={G:|V(G)|=sat(n,P_m^2) and G a P_m^2-saturated graph}. All graphs in Sat(n,P_m^2) are obtained computationally for n≤8 and m≤8 and expressed by their degree sequence.
Courses Scheduling using Graph Labeling Ramdani, Rismawati; Nursyahida, Salwa
KUBIK Vol 10 No 1 (2025): IN PRESS
Publisher : Jurusan Matematika, Fakultas Sains dan Teknologi, UIN Sunan Gunung Djati Bandung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15575/kubik.v10i1.44243

Abstract

At the beginning of each academic semester, universities are routinely required to develop course schedules that minimize or eliminate conflicts. Scheduling conflicts typically arise when multiple courses are taught by the same lecturer, taken by the same group of students, or require the use of the same classroom. As a result, an efficient and systematic method is needed to generate conflict-free schedules while optimizing the use of available time slots. One alternative approach is to apply graph theory, particularly graph coloring techniques, to the scheduling process. In this approach, each course is represented as a vertex in a graph, and an edge is established between two vertices if the corresponding courses cannot be held simultaneously. Graph coloring is then used to assign different time slots (represented as colors) to adjacent vertices, ensuring that no conflicting courses are scheduled at the same time. This paper proposes a course scheduling algorithm based on graph coloring, aiming to produce feasible schedules that reduce conflicts and enhance resource utilization. The approach provides a mathematical framework that can support automated and scalable scheduling systems in academic institutions.
Co-Authors Esih Sukaesih, Esih Rana, Salsabiil Rismawati Ramdani