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Week
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Topics
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Study Metarials
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1
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Basic concepts related to graphs
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R1. Section 1
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2
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Fuzzy sets and Fuzzy relations
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R2. Section 1
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3
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Definition of Fuzzy graphs and basic concepts of fuzzy graph
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R3. Section 1.1,1.2,1.3,1.4 ve 1.5
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4
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Automorphism and Isomorphism of Fuzzy Graphs
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R3. Section 1.6
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5
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Complement of Fuzzy Graph
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R3. Section 1.7
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6
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Regular and Irregular Fuzzy Graphs
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R3. Section 1.8
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7
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Union, Join and Composition of Fuzzy Graphs
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R3. Section 1.9.1, 1.9.2, 1.9.3
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8
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Direct, semi-strong and strong products of Fuzzy Graphs
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R3.Section 1.9.4, 1.9.5, 1.9.6
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9
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Cartesian, Tensor, Normal, Modular and Homomorphic products of Fuzzy Graphs
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R3. Section 1.9.7, 1.9.8, 1.9.9, 1.9.10, 1.9.11
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10
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Matrix Representation of Fuzzy Graphs
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R3.Section 1.10
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11
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Balanced Fuzzy Graphs and Cliques in Fuzzy Graphs
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R3. Section 1.11, 1.12
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12
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Independent Sets and Domination in Fuzzy Graphs
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R3.Section 1.13, 1.14
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13
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Eigenvalues and Energy of Fuzzy Graphs
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R3. Section 1.15
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14
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Extension of Fuzzy Graphs
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R3.Section 1.17
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Prerequisites
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-
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Language of Instruction
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Turkish
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Responsible
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Assoc. Prof. Dr. Faruk KARAASLAN
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Instructors
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-
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Assistants
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-
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Resources
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R1.Büyükköse, Ş., & Gök, G. K. (2018). Graf Teoriye Giriş.
R2. Mordeson, J. N., & Nair, P. S. (2012). Fuzzy graphs and fuzzy hypergraphs (Vol. 46). Physica.
R3. Pal, M., Samanta, S., & Ghorai, G. (2020). Modern trends in fuzzy graph theory (pp. 7-93). Springer
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Supplementary Book
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SR1. Paksoy, T., Pehlivan, N. Y., & Özceylan, E. (2013). Bulanık küme teorisi. Nobel Yayın: Ankara.
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Goals
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To teach the structure of fuzzy graphs, basic concepts of fuzzy graphs and operations between fuzzy graphs
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Content
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Fuzzy graphs, product operations of fuzzy graphs, Automorphism and isomorphism of fuzzy graphs, matrix representation of fuzzy graphs and eigenvalues, extensions of fuzzy graphs
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Program Learning Outcomes |
Level of Contribution |
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1
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Improve and deepen the gained knowledge in Mathematics in the speciality level
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3
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2
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Use gained speciality level theoretical and applied knowledge in mathematics
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3
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3
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Perform interdisciplinary studies by relating the gained knowledge in Mathematics with other fields.
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3
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4
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Analyze mathematical problems by using the gained research methods
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2
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5
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Conduct independently a study requiring speciliaty in Mathematics
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-
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6
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Develop different approaches and produce solutions by taking responsibility to problems encountered in applications
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-
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7
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Evaluate the gained speciality level knowledge and skills with a critical approach and guide the process of learning
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-
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8
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Transfer recent and own research related to mathematics to the expert and non-expert shareholders written, verbally and visually
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-
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9
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Uses computer software and information technologies related to the field of mathematics at an advanced level.
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-
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10
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Have the awareness of acting compatible with social, scientific, cultural and ethical values during the process of collecting, interpreting, applying and informing data related to Mathematics
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-
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