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The number of edges in a regular graph of degree $d$ and $n$ vertices is ____________
in Graph Theory by Veteran (52.1k points)
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Consider the example of complete graph, In a complete graph which is $(n-1)$ regular (where n is the no of vertices) has edges $\frac{n(n-1)}{2}$
$n$ vertices are adjacent to $n-1$ vertices and an edge contributes two degree so dividing by $2$.

$d*n = 2*|E|$
Therefore, in $d$ regular graph No of edges will be $\frac{n*d}{2}$
 

by Boss (43.5k points)
edited by
+2 votes

In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency.

In the given que, no. of vertices= n

deg of each vertices= d (no. of neighbor of each vertices)

 total edges= n*(no. of neighbor)/2= (n*d)/2

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