deg v (degree of the vertex v in an undirected graph)
In graph theory, the degree of a vertex is the number of edges incident to that vertex
In graph theory, the degree of a vertex is the number of edges incident to that vertex. In an undirected graph, a vertex can have both incoming and outgoing edges. The degree of a vertex is denoted as deg(v), where v represents the vertex.
To find the degree of a vertex in an undirected graph, you count the number of edges that are connected to that vertex. For example, if a vertex is connected to 3 other vertices by edges, then the degree of that vertex is 3.
The degree of a vertex is an important concept in graph theory as it provides valuable information about the connectivity and structure of the graph. It can help determine the center or peripheral vertices, or identify certain properties such as whether the graph is connected or bipartite.
For instance, in a social network graph where each person represents a vertex and the connections between them represent edges, the degree of a person’s vertex would indicate the number of friends they have.
Overall, the degree of a vertex is a fundamental concept in graph theory that plays a crucial role in analyzing graphs and their properties.
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