Question

Consider an undirected graph G = (V, E). The degree of a vertex v is the

number of edges adjacent to v—that is, the number of edges of the form (v,u) ∈ E. Recall the
standard notational convention that n = |V | and m = |E|.

Answer 1

The question pertains to graph theory in mathematics, specifically regarding the degree of a vertex within an undirected graph, which is the count of adjacent edges to the vertex.

Step-by-step explanation:

The student's question references an undirected graph G = (V, E), where 'n' represents the number of vertices (|V|) and 'm' represents the number of edges (|E|). In such a graph, the degree of a vertex 'v' is the count of how many edges are adjacent to it. This is a fundamental concept in graph theory, which is a significant area of study within discrete mathematics and computer science.

To find the degree of a vertex 'v', you would simply count all the edges that have 'v' as one end of the edge. In the context of the overall discipline, understanding the idea of the degree of a vertex helps in analyzing graphs for patterns, structural properties, and algorithms applicable to network analysis.

For example, in a graph with vertices V = {v1, v2, v3} and edges E = {(v1, v2), (v2, v3)}, the degree of vertex v2 would be 2 because it is adjacent to both v1 and v3 via two separate edges.