In a digraph, the sum of the in-degrees is equal to:A. The number of verticesB. The number of edgesC. Twice the number of verticesD. Twice the number of edges
Question
In a digraph, the sum of the in-degrees is equal to:
A. The number of vertices
B. The number of edges
C. Twice the number of vertices
D. Twice the number of edges
Solution
The correct answer is B. The number of edges.
Here's why:
In a directed graph (or digraph), each edge has an initial vertex and a terminal vertex. The in-degree of a vertex is the number of edges for which that vertex is the terminal vertex.
If you sum the in-degrees of all vertices in the digraph, you're essentially counting all edges, because each edge contributes exactly 1 to the total sum of in-degrees (it increases the in-degree of its terminal vertex by 1).
Therefore, in a digraph, the sum of the in-degrees is equal to the number of edges.
Similar Questions
In a simple graph, the number of edges is equal to twice the sum of the degrees of the vertices.Group of answer choicesFalseTrue
What is the value of the sum of the minimum in-degree and maximum out-degree of an Directed Acyclic Graph?
The number of edges in a complete graph 𝐾𝑛K n is:A. 𝑛nB. 𝑛−1n−1C. 𝑛(𝑛−1)22n(n−1) D. 2𝑛2n
If a graph has 8 vertices and 12 edges, then the degree of each vertex in the graph is:a.3b.6c.12d.10
For which of the following combinations of the degrees of vertices would the connected graph be Eulerian?Select one:a.1,2,3b.2,3,4c.2,4,5d.1,3,5
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.