Sum of Degrees of Vertices Theorem


If G = (V, E) be a non-directed graph with vertices V = {V1, V2,…Vn} then

n ∑ i=1 deg(Vi) = 2|E|

Corollary 1

If G = (V, E) be a directed graph with vertices V = {V1, V2,…Vn}, then

n ∑ i=1 deg+(Vi) = |E| = n ∑ i=1 deg(Vi)

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|

Updated on: 26-Aug-2019

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