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# Sum of Degrees of Vertices Theorem

If G = (V, E) be a non-directed graph with vertices V = {V_{1}, V_{2},…V_{n}} then

n ∑ i=1 deg(V

_{i}) = 2|E|## Corollary 1

If G = (V, E) be a directed graph with vertices V = {V_{1}, V_{2},…V_{n}}, then

n ∑ i=1 deg

^{+}(V_{i}) = |E| = n ∑ i=1 deg^{−}(V_{i})## Corollary 2

In any non-directed graph, the number of vertices with Odd degree is Even.

## Corollary 3

In a non-directed graph, if the degree of each vertex is k, then

k|V| = 2|E|

## Corollary 4

In a non-directed graph, if the degree of each vertex is at least k, then

k|V| = 2|E|

## Corollary 5

In a non-directed graph, if the degree of each vertex is at most k, then

k|V| = 2|E|

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