Handshake Lemma

- finite undirected gragh

∑deg(v) = 2|E|

In a k-ary tree where every node has either 0 or k children, following property is always true.

L = (k - )*I +
Where L = Number of leaf nodes
      I = Number of internal nodes

case: root is leaf/internal node

Sum of all degrees  =  * (Sum of Edges)

L + (I-)*(k+) + k =  * (L + I - )
L + k*I - k + I - + k = *L  + 2I -
L + K*I + I -  = *L + *I -
K*I +  - I = L
(K-)*I +  = L 

https://www.geeksforgeeks.org/handshaking-lemma-and-interesting-tree-properties/