Enhance Your Learning with Graph Theory Flash Cards for quick learning
A mathematical structure consisting of a set of vertices and a set of edges that connect pairs of vertices.
A fundamental unit of a graph, often represented by a point or a node.
A connection between two vertices in a graph, often represented by a line or an arc.
A square matrix used to represent a finite graph, where the elements indicate whether pairs of vertices are adjacent or not.
The number of edges incident to a vertex in a graph.
A sequence of edges that allows you to travel from one vertex to another in a graph.
A path that starts and ends at the same vertex in a graph.
A graph in which there is a path between every pair of vertices.
A graph in which there is no path between at least one pair of vertices.
A graph in which there is an edge between every pair of distinct vertices.
A graph whose vertices can be divided into two disjoint sets such that every edge connects a vertex from one set to a vertex from the other set.
A graph that contains a closed trail that includes every edge exactly once.
A graph that contains a closed path that includes every vertex exactly once.
A connected acyclic graph, where there is exactly one path between any pair of vertices.
A subgraph of a graph that is a tree and includes all the vertices of the original graph.
A graph that can be drawn on a plane without any edges crossing.
The minimum number of colors needed to color the vertices of a graph such that no two adjacent vertices have the same color.
A directed graph where each edge has a capacity and represents the maximum amount of flow that can pass through it.
The maximum amount of flow that can be sent from a source vertex to a sink vertex in a flow network.
A cut in a flow network that partitions the vertices into two disjoint sets, the source set and the sink set, with the minimum capacity across the cut.
An algorithm for finding the shortest paths between nodes in a graph.
An algorithm for finding the shortest paths between nodes in a graph with negative edge weights.
An algorithm for finding a minimum spanning tree for a weighted undirected graph.
An algorithm for finding a minimum spanning tree for a weighted undirected graph.
An ordering of the vertices of a directed graph such that for every directed edge (u, v), vertex u comes before vertex v in the ordering.
A graph traversal algorithm that explores all the vertices of a graph in breadth-first order.
A graph traversal algorithm that explores all the vertices of a graph in depth-first order.
A set of vertices in a directed graph where there is a directed path between every pair of vertices.
A vertex in a graph whose removal increases the number of connected components.
A maximal subgraph of a graph that is connected and has no articulation points.
A path in a graph that visits every edge exactly once.
A path in a graph that visits every vertex exactly once.
A tree that spans all the vertices of a connected, undirected graph with the minimum possible total edge weight.
A problem in graph theory that asks for the shortest possible route that visits each vertex exactly once and returns to the starting vertex.
A relation between two graphs that preserves their adjacency structure.
Assigning colors to the vertices of a graph such that no two adjacent vertices have the same color.
A set of edges in a graph where no two edges share a common vertex.
A vertex in a graph whose removal increases the number of connected components.
An edge in a graph whose removal increases the number of connected components.
Algorithms designed to solve problems related to graphs, such as finding shortest paths, minimum spanning trees, and more.
The practical use of graph theory in various fields, including computer science, social networks, transportation networks, and more.
A database that uses graph structures for semantic queries with nodes, edges, and properties to represent and store data.
A type of neural network designed to process and analyze graph-structured data.
The process of creating visual representations of graphs to better understand their structure and relationships.
The ongoing study and exploration of new concepts, algorithms, and applications in the field of graph theory.
Recommended books and resources for learning and studying graph theory in-depth.
Online and offline courses that cover the fundamentals and advanced topics of graph theory.
Step-by-step tutorials and guides to help beginners understand and apply graph theory concepts.
Test your knowledge of graph theory with interactive quizzes and practice questions.