Akademik Dersler - İçerik

Will be able to explain the fundamental concepts and representations of graph theory.
Defines the concepts of graph, subgraph, degree, and connectivity.
Represents graphs using adjacency lists and adjacency matrices.
Formulates problems using graph models.
Will be able to analyze fundamental algorithms on graphs.
Applies depth-first search (DFS) and breadth-first search (BFS) algorithms.
Analyzes the time and space complexity of algorithms.
Compares graph algorithms with respect to different data structures.
Will be able to solve problems related to spanning trees and their optimizations.
Explains the fundamental properties of spanning trees.
Finds minimum spanning trees using Kruskal’s and Prim’s algorithms.
Explains methods for determining the number of spanning trees.
Will be able to analyze structural properties and special classes of graphs.
Explains planar graphs and Euler’s formula.
Interprets matching problems in graphs and Hall’s theorem.
Evaluates existence conditions for Eulerian and Hamiltonian structures.
Will be able to model graph problems and develop solution approaches.
Formulates Eulerian, Hamiltonian, and traveling salesman problems.
Analyzes graph coloring, independent set, and clique problems.
Selects and applies appropriate graph algorithms for a given problem.
Will be able to evaluate the computational complexity of graph problems.
Explains the classes P and NP and the differences between them.
Interprets the concept of NP-completeness and reducibility.
Evaluates the complexity of independent set, clique, Hamiltonian cycle, and graph coloring problems.