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- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/05%3A_Graph_Theory/5.04%3A_PathsThis page discusses key concepts in graph theory, including definitions of walks, trails, and paths, highlighting their distinct characteristics regarding vertex and edge repetition. It explains Euler...This page discusses key concepts in graph theory, including definitions of walks, trails, and paths, highlighting their distinct characteristics regarding vertex and edge repetition. It explains Eulerian trails and Hamiltonian paths and addresses graph connectivity, stating that a graph is connected if any vertex pair has a connecting path. Additionally, it introduces n-connected graphs and includes practice checkpoints to reinforce understanding of these concepts.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/05%3A_Graph_Theory/5.05%3A_CyclesThis page defines important graph theory terms such as circuit, cycle, Eulerian circuit, and Hamiltonian circuit. It explains that a circuit is a closed walk with the same starting and ending vertex, ...This page defines important graph theory terms such as circuit, cycle, Eulerian circuit, and Hamiltonian circuit. It explains that a circuit is a closed walk with the same starting and ending vertex, while a cycle does not repeat vertices. An Eulerian circuit covers every edge once, and a Hamiltonian circuit visits each vertex once. Additionally, it offers practice checkpoints for readers to engage with the concepts, including drawing cycles and identifying specific types of circuits.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_300%3A_Mathematical_Ideas_Textbook_(Muranaka)/06%3A_Miscellaneous_Extra_Topics/6.04%3A_Graph_Theory/6.4.00%3A_Graph_TheorySome definitions are important to understand before delving into Graph Theory: (1) A graph is a picture of dots called vertices and lines called edges. (2) An edge that starts and ends at the same ver...Some definitions are important to understand before delving into Graph Theory: (1) A graph is a picture of dots called vertices and lines called edges. (2) An edge that starts and ends at the same vertex is called a loop. (3) If there are two or more edges directly connecting the same two vertices, then these edges are called multiple edges. (4) If there is a way to get from one vertex of a graph to all the other vertices of the graph, then the graph is connected, otherwise it is disconnected.
- https://math.libretexts.org/Courses/Florida_SouthWestern_State_College/MGF_1131%3A_Mathematics_in_Context__(FSW)/07%3A_Graph_Theory/7.01%3A_Basic_Graphs_and_Graphs_StructureThis section introduces graph theory, defining graphs, vertices, and edges, and distinguishing simple graphs from multigraphs. It explores vertex classification, degrees, and various graph types like ...This section introduces graph theory, defining graphs, vertices, and edges, and distinguishing simple graphs from multigraphs. It explores vertex classification, degrees, and various graph types like complete and isomorphic graphs. Key concepts include walks, trails, paths, and graph connectivity, with applications in real-world scenarios such as Page Rank and fraud detection.
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Book%3A_College_Mathematics_for_Everyday_Life_(Inigo_et_al)/06%3A_Graph_Theory/6.01%3A_Graph_TheorySome definitions are important to understand before delving into Graph Theory: (1) A graph is a picture of dots called vertices and lines called edges. (2) An edge that starts and ends at the same ver...Some definitions are important to understand before delving into Graph Theory: (1) A graph is a picture of dots called vertices and lines called edges. (2) An edge that starts and ends at the same vertex is called a loop. (3) If there are two or more edges directly connecting the same two vertices, then these edges are called multiple edges. (4) If there is a way to get from one vertex of a graph to all the other vertices of the graph, then the graph is connected, otherwise it is disconnected.
- https://math.libretexts.org/Courses/Florida_SouthWestern_State_College/MGF_1131%3A_Mathematics_in_Context__(FSW)/07%3A_Graph_Theory/7.04%3A_TreesThis section covers trees in graph theory, defining them as connected acyclic graphs and exploring their significance in applications like family trees and computer networks. It discusses spanning tre...This section covers trees in graph theory, defining them as connected acyclic graphs and exploring their significance in applications like family trees and computer networks. It discusses spanning trees, including methods for their construction, emphasizing Kruskal's algorithm for finding minimum spanning trees to minimize connection costs. Key characteristics of spanning trees are highlighted, including their cycle-free nature and connection of all vertices.
