Question 8119 – Regular-Language
December 6, 2023Question 10018 – Theory-of-Computation
December 6, 2023Question 1585 – Nielit Scientist-B IT 22-07-2017
Given an undirected graph G with V vertices and E edges, the sum of the degrees of all vertices is
Correct Answer: B
Question 1 Explanation:
Theorem (Sum of Degrees of Vertices Theorem):
Suppose a graph has n vertices with degrees d 1 , d 2 , d 3 , …, d n.
Add together all degrees to get a new number
d 1 + d 2 + d 3 + . .. + d n = D v . Then D v = 2 e .
In words, for any graph the sum of the degrees of the vertices equals twice the number of edges.
Suppose a graph has n vertices with degrees d 1 , d 2 , d 3 , …, d n.
Add together all degrees to get a new number
d 1 + d 2 + d 3 + . .. + d n = D v . Then D v = 2 e .
In words, for any graph the sum of the degrees of the vertices equals twice the number of edges.
E
2E
V
2V
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