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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|
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