The number of edges in a regular graph of degree 'd' and 'n' vertices is:

To determine the number of edges in a regular graph, we apply the Handshaking Lemma from graph theory. This fundamental principle states that the sum of degrees of all vertices in any undirected graph is exactly equal to twice the number of edges. In a regular graph with 'n' vertices where every vertex has the same degree 'd', we first calculate the total sum of degrees by multiplying the number of vertices by the degree of each vertex, resulting in n × d. Since this sum represents twice the number of edges (2E), we solve for E by dividing the total degree sum by 2. Therefore, the number of edges is (nd)/2.",