Concept
The degree of a vertex in a graph is the number of edges incident to the vertex, which provides insight into the vertex's connectivity within the graph. In directed graphs, the degree is split into in-degree and out-degree, representing incoming and outgoing edges, respectively.
Relevant Degrees
Concept
An Eulerian Path is a trail in a graph that visits every edge exactly once, and it exists if and only if the graph is connected and has exactly zero or two vertices of odd degree. If a graph has exactly two vertices of odd degree, any Eulerian Path will start at one of these vertices and end at the other.
Concept
Vertices and edges are fundamental components of graph theory, where vertices (or nodes) represent entities and edges signify the connections between them. Understanding the relationship and properties of vertices and edges is crucial for analyzing graph structures and solving problems related to networks, paths, and connectivity.
Concept
An undirected graph is a set of nodes connected by edges, where the edges have no direction, meaning the connection is bidirectional. This type of graph is used to model relationships where mutual interaction is possible, such as social networks or undirected communication pathways.
Concept
A vertex is a fundamental element in geometry and graph theory, representing a corner or intersection point where two or more lines, edges, or curves meet. In the context of graphs, a vertex is a node that may connect to other vertices via edges, playing a crucial role in the structure of networks and geometric shapes.
Concept
An Eulerian Circuit is a closed path in a graph that visits every edge exactly once and returns to the starting vertex. A connected graph has an Eulerian Circuit if and only if every vertex has an even degree.
3